The materials to prepare students for

The materials to prepare students for practical lessons of inorganic chemistry

LESSON № 3.

Themes: 5. The structure of an atom.

6. The periodic law of Mendeleyev D.I.

7. The nature of chemical bonds and the structure of compounds.

Plan

1. Basic theory of atomic structure (x-rays cathode-rays, radio-activity). Planetary model of atom.

2. Planck’s equation. Bohr’ postulates. The structure of an atom of hydrogen by Bohr’ theory position. Wave-particle duality of electron, electronic orbital, Heisenberg’s uncertainty principle. The Schrodinger wave equation.

3.  Quantum numbers. Aufbau principle (Hund’s rules and the Pauli exclusion principle).

4. The periodic law of Mendeleyev D.I. and it modern interpretation. Structure of the periodic system. Type of the periodic system. Periodic properties of elements.

5. The mechanism of formation of chemical bonds. The types of chemical bonds, it property.

6.  The mechanisms of formation of the covalent bond and it properties. The valence bond theory.

7. The hybridization of atomic orbitals. Spatial structure of molecules. Polar and unpolar molecules. An ionic bond.

8. The method of molecular orbitals (MO). The types of МО and their properties. Multipleness of bond in ММО. Intermolecular interaction. A hydrogen bond.

 

1. Basic theory of atomic structure (x-rays cathode-rays, radio-activity). Planetary model of atom.

The word atom is a Greek word meaning indivisible, i.e., an ultimate particle which cannot be further subdivided. The idea that all matter ultimately consists of extremely small particles was conceived by ancient Indian and Greek philosophers. The old concept was put on firm footing by John Dalton in the form of atomic theory which he developed in the years 1803–1808. This theory was a landmark in the history of chemistry. According to this theory, atom is the smallest indivisible part of matter which takes part in chemical reactions. Atom is neither created nor destroyed. Atoms of the same element are similar in size, mass and characteristics; however, atoms of different elements have different size, mass and characteristics.

In 1833, Michael Faraday showed that there is a relationship between matter and electricity. This was the first major break-through to suggest that atom was not a simple indivisible particle of all matter but was made up of small particles. Discovery of electrons, protons and neutrons discarded the indivisible nature of the atom proposed by John Dalton.

The complexity of the atom was further revealed when the following discoveries were made in subsequent years.

During the past 100 years, scientists have made contributions which helped in the development of modern theory of atomic structure. The works of J.J. Thomson and Ernst Rutherford actually laid the foundation of the modern picture of the atom. It is now believed that the atom consists of several particles called sub-atomic particles like electron, proton, neutron, positron, neutrino, meson, etc. Out of these particles, the electron, the proton and the neutron are called fundamental particles and are the building blocks of the atoms.

Cathode rays—Discovery of Electron

The nature and existence of electron was established by experiments on conduction of electricity through gases. In 1859, Julius Plucker started the study of conduction of electricity through gases at low pressure in a discharge tube. [A common discharge tube consists of a hard glass cylindrical tube (about 50 cm long) with two metal electrodes sealed on both the ends. It is connected to a side tube through which it can be evacuated to any desired pressure with the help of a vacuum pump.] Air was almost completely removed from the discharge tube (pressure about 10^-4 atmosphere). When a high voltage of the order of 10,000 volts or more was impressed across the electrodes, some sort of invisible rays moved from the negative electrode to the positive electrode (Fig. 1). Since the negative electrode is referred to as cathode, these rays were called cathode rays. Further inverstigations were made by W. Crookes, J. Perrin, J. J. Thomson an others. Cathode rays possess the following properties:

1. They travel in straight lines away from the cathode with very high velocities ranging from 10⁹ ‑ 10¹¹ cm per second. A shadow of metallic object placed in the path is cast on the wall opposite to the cathode.

2. They produce a green glow when strike the glass wall beyond the anode. Light is emitted when they strike the zinc sulphide screen.

3. They produce heat energy when they collide with the matter. It shows that cathode rays possess kinetic energy which is converted into heat energy when stopped by matter.

4. They are deflected by the electric and magnetic fields. When the rays are passed between two electrically charged plates, these are deflected towards the positively charged plate. They discharge a positively charged gold leaf electroscope. It shows that cathode rays carry negative charge.

5. They possess kinetic energy. It is shown by the experiment that when a small pin wheel is placed in their path, the blades of the wheel are set in motion. Thus, the cathode rays consist of material particles which have mass and velocity. These particles carrying negative charge were called negatrons by Thomson. The name `negatron’ was changed to `electron’ by Stoney.

6. Cathode rays produce X-rays. When these rays fall on material having high atomic mass, new type of penetrating rays of very small wavelength are emitted which are called X-rays.

7. These rays affect the photographic plate.

8. These rays can penetrate through thin foils of solid materials and cause ionisation in gases through which they pass.

9. The nature of the cathode rays is independent of:

·         the nature of the cathode;

·          the gas in the discharge tube.

In 1897, J. J. Thomson determined the e/m value (charge/mass) of the electron by studying the deflections of cathode rays in electric and magnetic fields. The value of e/m has been found to be 1.7588 × 10⁸ coulomb/g.

where

e = charge on electron

m = mass of electron

By performing a series of experiments, Thomson proved that whatever gas be taken in the discharge tube and whatever be the material of the elecrodes, the value of e/m is always the same. Electrons are thus common universal constituents of all atoms.

J.J. Thomson gave following relation to calculate charge/mass ratio, where the terms have usual significance given before = -1.7588 × 10¹¹ C kg^-1

Electrons are also produced by the action of ultraviolet light or X-rays on metal and from heated filaments. b-particles emitted by radioactive materials are also electrons.

The first precise measurement of the charge on the electron was made by Robert A. Millikan in 1909 by oil drop experiment. The charge on the electron was found to be -1.6022 × 10^-19 coulomb. Since an electron has the smallest charge known, it was, thus, designated as unit negative charge.

Mass of the electron: The mass of the electron can be calculated from the value of e/m and the value of e.

 

= 9.1096 × 10^-28 g or 9.1096 × 10^-31 kg

This is termed as the rest mass of the electron, i.e., mass of the electron when moving with low speed. The mass of a moving electron may be calculated by applying the following formula:

Mass of moving electron = IMG,

where is the velocity of the electron and c is the velocity of light. When becomes equal to c, mass of the moving electron becomes infinity and when the velocity of the electron becomes greater than c mass of the electron becomes imaginary.

Mass of the electron relative to that of hydrogen atom:

Mass of hydrogen atom = 1.008 amu

= 1.008 × 1.66 × 10^-24 g (since 1 amu = 1.66 × 10^-24 g)

= 1.673 × 10^-24 g

 

Thus, Mass of an electron = × mass of hydrogen atom = 0.000549 amu

An electron can, thus, be defined as a sub-atomic particle which carries charge -1.60 × 10^-19 coulomb, i.e., one unit negative charge and has mass 9.1 × 10^-28 g, i.e., mass of the hydrogen atom (0.000549 amu).

Millikan’s oil drop method is used to determine the charge on an electron by measuring the terminal velocity of a charged spherical oil-drop which is made stationary between two electrods on which a very high potential is applied, where = coefficient of viscosity of the gas medium

 

Positive Rays – Discovery of Proton

With the discovery of electrons, scientists started looking for positively charged particles which were naturally expected because matter is electrically neutral under ordinary conditions. The first experiment that led to the discovery of the positive particle was conducted by Goldstein in 1886. He used a perforated cathode in the modified cathode ray tube (Fig. 2). It was observed that when a high potential difference was applied between the electrodes, not only cathode rays were produced but also a new type of rays were produced simultaneously from anode moving towards cathode and passed through the holes or canals of the cathode. These rays were termed canal rays since these passed through the canals of the cathode. These were also named anode rays as these originated from anode. When the properties of these rays were studied by Thomson, he observed that these rays consisted of positively charged particles and named them as positive rays.

The following characteristics of the positive rays were recognised:

1. The rays travel in straight lines and cast a shadow of the object placed in their path.

2. Like cathode rays, these rays also rotate the wheel placed in their path and also have heating effect. Thus, the rays possess kinetic energy, i.e., mass particles are present.

3. The rays produce flashes of light on zinc sulphide screen.

4. The rays are deflected by electric and magnetic fields in a direction opposite to that of cathode rays. These rays are attracted towards the negatively charged plate showing thereby that these rays carry positive charge.

5. These rays can pass through thin metal foils.

6.  These rays can produce ionisation in gases.

7. These rays are capable of producing physical and chemical changes.

8. Positive particles in these rays have e/m values much smaller than that of electron. This means either m is high or the value of charge is small in comparison to electron. Since positive particle is formed by the loss of electron or electrons, the charge on the positive particle must be an integral multiple of the charge present on the electron. Hence, for a smaller value of e/m, it is definite that positive particles possess high mass.

9. e/m value is dependent on the nature of the gas taken in the discharge tube, i.e., positive particles are different in different gases.

Accurate measurements of the charge and the mass of the particles obtained in the discharge tube containing hydrogen, the lightest of all gases, were made by J.J. Thomson in 1906. These particles were found to have the e/m value as + 9.579 × 104 coulomb/g. This was the maximum value of e/m observed for any positive particle. It was thus assumed that the positive particle given by hydrogen represents a fundamental particle of positive charge. This particle was named proton by Rutherford in 1911. Its charge was found to be equal in magnitude but opposite in sign to that of electron.

Thus, proton carries a charge + 1.602 × 10^–19 coulomb, i.e., one unit positive charge.

The mass of the proton, thus, can be calculated.

A proton is defined as a sub-atomic particle which has a mass nearly 1 amu and a charge of +1 unit (+1.602 × 10^–19 coulomb).

Protons are produced in a number of nuclear reactions. On the basis of such reactions, proton has been recognised as a fundamental building unit of the atom.

Rutherford Experiment– Discovery of Nucleus

After the discovery of electron and proton, the question arose how these charged particles are distributed in an atom. The answer was given by J.J. Thomson in the form of first model of the atom.

He proposed that the positive charge is spread over a sphere in which the electrons are embedded to make the atom as a whole neutral. This model was much like resins in a pudding and is also known as Thomson’s plum pudding model. This model was discarded as it was not consistent with the results of further investigations such as scattering of a-particles by thin metal foils.

In 1911, Ernst Rutherford and his co-workers carried out a series of experiments using -particles* (Fig. 3 and 4). A beam of -particles was directed against a thin foil of about 0.0004 cm thickness of gold, platinum, silver or copper respectively. The foil was surrounded by a circular fluorescent zinc.

The radiations emitted by radioactive substances consist of -particles. These particles are positively charged. These particles are actually helium atoms from which electrons have been removed. Each -particle consists of a mass equal to about 4 times that of hydrogen atom and carries a positive charge of two units. It is represented by the symbol a or ⁴₂He.

-particles are usually obtained from a natural isotope of polonium-214. sulphide screen. Whenever an a-particle struck the screen, it produced a flash of light.

The following observations were made:

1. Most of the -particles (nearly 99%) went straight without suffering any deflection.

2. A few of them got deflected through small angles.

3. A very few (about one in 20,000) did not pass through the foil at all but suffered large deflections (more thant 90°) or even came back in more or less the direction from which they have come, i.e., a deflection of 180°.

Consider an -particle of mass `m‘ moving directly towards a nucleus with velocity at any given time. As this particle approaches the nucleus, its velocity and hence kinetic energy continues to decrease. At a certain distance r₀ from the nucleus, the -particle will stop and then start retracing its path depicted. This distance is called the distance of closest approach. At this distance, the kinetic energy of the -particle is transformed into electrostatic potential energy.

Here, the distance of closest approach is of the order of 10_-14 m. So, the radius of the nucleus should be less than 10_-14 m.

Following conclusions were drawn from the above observations:

1. Since most of the a-particles went straight through the metal foil undeflected, it means that there must be very large empty space within the atom or the atom is extra-ordinarily hollow.

2. A few of the -particles were deflected from their original paths through moderate angles; it was concluded that whole of the positive charge is concentrated and the space occupied by this positive charge is very small in the atom. When -particles come closer to this point, they suffer a force of repulsion and deviate from their paths.

The positively charged heavy mass which occupies only a small volume in an atom is called nucleus. It is supposed to be present at the centre of the atom.

A very few of the -particles suffered strong deflections or even returned on their path indicating that the nucleus is rigid and -particles recoil due to direct collision with the heavy positively charged mass. The graph between angle of scattering and the number of a-particles scattering in the corresponding direction is as shown in Fig. 4(b).

Moseley Experiment ‑ Atomic Number

Roentgen, in 1895, discovered that when high energy electrons in a discharge tube collide with the anode, penetrating radiations are produced which he named X-rays.

X-rays are electromagnetic radiations of very small wave-lengths (0.1–20 Å). X-rays are diffracted by diffraction gratings like ordinary light rays and X-ray spectra are, thus, produced.

Each such spectrum is a characteristic property of the element used as anode.
Moseley (1912–13), investigated the X-ray spectra of 38 different elements, starting from aluminium and ending in gold. He measured the frequency of principal lines of a particular series (the a-lines in the K series) of the spectra. It was observed that the frequency of a particular spectral line gradually increased with the increase of atomic mass of the element. But, it was soon realised that the frequency of the particular spectral line was more precisely related with the serial number of the element in the periodic table which he termed as atomic number (Z). He presented the following relationship.

√v=a(Z-b)

where = frequency of X-rays, Z = atomic number, a and b are constants. When the values of square root of the frequency were plotted against atomic numbers of the elements producing X-rays, a straight line was obtained.

van den Broek (1913) pointed out that the atomic number of an element is equal to the total positive charge contained in the nucleus of its atom. Rutherford was also having the same opinion that the atomic number of an element represents the number of protons in the nucleus of its atom. Thus, Atomic number of the element = Serial number of the element in periodic table = Charge on the nucleus of the atom of the element = Number of protons present in the nucleus of the atom of the element = Number of extranuclear electrons present in the atom of the element

Discovery of Neutron

The discovery of neutron was actually made about 20 years after the structure of atom was elucidated by Rutherford. Atomic masses of different atoms could not be explained if it was accepted that atoms consisted only of protons and electrons. Thus, Rutherford (1920) suggested that in an atom, there must be present at least a third type of fundamental particles which should be electrically neutral and possess mass nearly equal to that of proton. He proposed the name for such fundamental particle as neutron. In 1932, Chadwick bombarded beryllium with a stream of -particles. He observed that penetrating radiations were produced which were not affected by electric and magnetic fields. These radiations consisted of neutral particles, which were called neutrons. The nuclear reaction can be shown as:

₄⁹Be + ₂⁴He₆¹²C + ₀¹n

The mass of the neutron was determined. It was 1.675 × 10^-24 g, i.e., nearly equal to the mass of proton.

Thus, a neutron is a sub-atomic particle which has a mass 1.675 × 10^-24 g, approximately 1 amu, or nearly equal to the mass of proton or hydrogen atom and carrying no electrical charge. The e/m value of a neutron is thus zero.

Rutherford Model

On the basis of scattering experiments, Rutherford proposed a model of the atom which is known as nuclear atomic model. According to this model:

1. An atom consists of a heavy positively charged nucleus where all the protons and neutrons are present. Protons and neutrons are collectively referred to as nucleons. Almost whole of the mass of the atom is contributed by these nucleons. The magnitude of the positive charge on the nucleus is different for different atoms.

2. The volume of the nucleus is very small and is only a minute fraction of the total volume of the atom. Nucleus has a diameter of the order of 10^-12 to 10^-13 cm and the atom has a diameter of the order of 10^-8 cm.

Thus, diameter (size) of the atom is 100,000 times the diameter of the nucleus*.

The radius of a nucleus is proportional to the cube root of the number of nucleons within it.

R = R₀A^1/3cm

where R₀ = 1.33 × 10^-13; A = mass number; R = Radius of the nucleus

Rutherford and Marsden calculated the density of the hydrogeucleus containing only one proton.

3. There is an empty space around the nucleus called extranuclear part. In this part electrons are present. The number of electrons in an atom is always equal to number of protons present in the nucleus. As the nucleus part of the atom is responsible for the mass of the atom, the extranuclear part is responsible for its volume. The volume of the atom is about 10¹⁵ times the volume of the nucleus.

4. Electrons revolve round the nucleus in closed orbits with high speeds. The centrifugal force acting on the revolving electrons is being counter balanced by the force of attraction between the electron and the nucleus.

This model was similar to the solar system, the nucleus representing the sun and revolving electrons as planets. The electrons are, therefore, generally referred to as planetary electrons.

1. The sun and the planets are very bit bodies and uncharged while the nucleus and electrons are very small

2.  The revolution of the planets in the solar system is governed by gravitational forces, while the revolution of electrons around the nucleus is governed by electrostatic forces.

3.  In the solar system, there is only one planet which revolves in any particular orbit, but in the nuclear atomic model more than one electron may ratate in any particular orbit.

Drawbacks of Rutherford model

1.  According to classical electromagnetic theory, when a charged particle moves under the influence of attractive force, it loses energy continuously in the form of electromagnetic radiations. Thus, when the electron (a charged particle) moves in an attractive field (created by protons present in the nucleus), it must emit radiations. As a result of this, the electron should lose energy at every turn and move closer and closer to the nucleus following a spiral path (Fig. 7). The ultimate result will be that it will fall into the nucleus, thereby making the atom unstable. Bohr made calculations and pointed out that an atom would collapse in 10^-8 seconds. Since the atom is quite stable, it means the electrons do not fall into the nucleus, thereby this model does not explain the stability of the atom.

2.  If the electrons lose energy continuously, the observed spectrum should be continuous but the actual observed spectrum consists of well defined lines of definite frequencies. Hence, the loss of energy by the electrons is not continuous in an atom.

1.  Atomic Number (Z). The atomic number of an element is the number of protons contained in the nucleus of the atom of that element.

2.  Nucleons. Protons and neutrons are present in a nucleus, so these fundamental particles are collectively known as nucleons.

3. Mass Number (A). The total number of protons and neutrons i.e., the number of nucleons present in the nucleus is called the mass number of the element.

4.  Nuclide. Various species of atoms in general. A nuclide has specific value of atomic number and mass number.

IUPAC notation of an atom ( nuclide). Let X be the symbol of the element, its atomic number be Z and mass number be A. Then the element can be represented as _zX^A.

5. lsotopes. Atoms of the element with same atomic number but different mass number e.g.₁H¹,₁H². There are three isotopes of hydrogen.

6. Isobars. Atoms having the same mass number but different atomic numbers, e.g.₁₅P³² and ₁₆S³² called isobars.

7.  Isotones. Atoms having the same number of neutrons but different number of protons or mass number, e.g.₆C¹⁴,₈O¹⁶ ,₇N¹⁵ are called isotones.

8. Isoelectronic. Atoms, molecules or ions having same number of electrons are isoelectronic e.g. (a) N₂CO,CN^–(b) N^-3, O^-2, F^–.

9.  Nuclear isomers (isomeric nuclei) are the atoms with the same atomic number and same mass number but with different radioactive properties. Example of nuclear isomers is Uranium-X( half life 1.4 min) and Uranium-Z ( half life 6.7 hours). The reason for nuclear isomerism is the different energy states of the two isomeric nuclei. Other examples are

Examples. CH ‑ CH and N₂ are isoelectronic because they contain same number of electrons (14) but they are not isosters whole benzene (C₆H₆) and Inorganic benzene (B₃N₃H₆) borazine are isosters because both contain same number of electrons and atoms.

10. Isosters. Molecules having same number of atoms and also same number of electrons are called isosters.

Examples.

1. N₂ and CO

2. CO₂ and N₂ O

3.  HCI and F₂

11. Atomic mass unit. It is exactly equal to 1/12 of the mass of ₆C¹²atom. 1amu = 1.66 x 10^-27 Kg. = 931.5 MeV

 

2. Planck’s equation. Bohr’ postulates. The structure of an atom of hydrogen by Bohr’ theory position. Wave-particle duality of electron, electronic orbital, Heisenberg’s uncertainty principle. The Schrodinger wave equation.

Nature of Electromagnetic Radiation (Electromagnetic wave Theory)

This theory was put forward by James Clark Maxwell in 1864. The main points of this theory are summed up as follows :

1. The energy is emitted from any source (like the heated rod or the filament of a bulb through which electric current is passed) continuously in the form of radiations (or waves) and is called the radiant energy.

2.  The radiations consist of electric and magnetic fields oscillating perpendicular to each other and both perpendicular to the direction of propagation of the radiation.

3. The radiations possess wave character and travel with the velocity of light (i.e. nearly 3 × 10⁸ m/sec). Because of the above characteristics, the radiations are called Electromagnetic radiations or Electromagnetic waves.

4. These waves do not require any material medium for propagation. For example, rays from the sun reach us through space which is a non-material medium.

Some important characteristics of a wave. The main characteristics of a wave are its wavelength (l), frequency (n) and velocity (c). These are defined as follows :

Wavelength of a wave is defined as the distance between any two consecutive crests or troughs. It is represented by and is expressed in Å or m or cm or nm (nanometer) or pm (picometer).

1 Å = 10^-8 cm = 10^-10 m

1 nm = 10^-9 m, 1 pm = 10^-12 m

Frequency of a wave is defined as the number of waves passing through a point in one second. It is represented by (nu) and is expressed in Hertz (Hz) or cycles/sec or simply sec^-1 or s^-1.

1 Hz = 1 cycle/sec

Velocity of a wave is defined as the linear distance travelled by the wave in one second. It is represented by c and is expressed in cm/sec or m/sec (m s^-1).

Besides the above three characteristics, two other characteristics of a wave are amplitude and wave number.

Amplitude of a wave is the height of the crest or the depth of the trough. It is represented by `a‘ and is expressed in the units of lenght.

Wave number is defined as the number of waves present in 1 cm length. Evidently, it will be equal to the reciprocal of the wavelength. It is represented by (read us nu bar).

Among various forms of visible light, violet colour has shortest wave length, highest freqiency and highest energy while red coloured light has borqest wavelength and least frequency.

If  is expressed in cm, will have the units cm^-1

Relationship between velocity, wavelength and frequency of a wave. As frequency is the number of waves passing through a point per second and is the length of each wave, hence their product will give the velocity of the wave. Thus

wave velocity (m/s) = frequency (Hz) x wavelength (m)

Electromagnetic spectrum. The different types of electromagnetic radiations differ only in their wavelength and hence frequencies. Their wavelengths increase in the following order :_

Cosmic rays < -rays < X-rays < Ultra-violet rays < Visible < Infrared < Micro waves < Radio waves

When these electromagnetic radiations are arranged in order of their increasing wavelengths or decreasing frequencies, the complete spectrum obtained is called electromagnetic spectrum.

Limitations of Electromagnetic Wave Theory. Electromagnetic wave theory was successful in explaining the properties of light such as interference, diffraction etc. but it could not explain the phenomena of `Black body radiation’, and `Photoelectric effect’ the discussion of which is beyond the scope of the book.

Study of Emission And Absorption Spectra.

We have studied above that the electromagnetic spectrum consists of radiations of different wave lengths and frequencies. An instrument used to separate the radiations of different wavelengths (or frequencies) is called spectroscope or a spectrograph. A spectroscope consists of a prism or a diffraction grating for the dispersion of radiations and a telescope to examine the emergent radiations with the human eye. However, if in a spectroscope, the telescope is replaced by a photographic film, the instrument is called a spectrograph and the photograph (or the pattern) of the emergent radiation recorded on the film is called a spectrogram or simply a spectrum of the given radiation.

Depending upon the source of radiation, the spectra are broadly classified into (i) Emission spectra and (ii) Absorption spectra. These are briefly explained below :

1. Emission spectra. When the radiation emitted from some source e.g. from the sun or by passing electric discharge through a gas at low pressure or by heating some substance to high temperature etc. is passed directly through the prism and then received on the photographic plate, the spectrum obtained is called ‘Emission spectrum’.

The emission spectra are mainly of two types:

(i) Continuous spectra When white light from any source such as sun, a bulb or any hot glowing body is analysed by passing through a prism, it is observed that it splits up into seven different wide bands of colours from violet to red, (like rainbow), as shown in Figure. These colours are so continuous that each of them merges into the next. Hence the spectrum is called continuous spectrum.

(ii) Line spectra When some volatile salt (e.g., sodium chloride) is placed in the Bunsen flame or an electric discharge is passed through a gas at low pressure, light is emitted. If this light is resolved in a spectroscope, it is found that no continuous spectrum is obtained but some isolated coloured lines are obtained on the photographic plate separated from each other by dark spaces. This spectrum is called ‘Line spectrum’.

-Each line in the spectrum corresponds to a particular wavelength. Further it is observed that each element gives its own characteristic spectrum, differing from those of all other elements. For example, sodium always gives two yellow lines (corresponding to wavelengths 5890 and 5896 Å). Hence the spectra of the elements are described as their finger prints differing from each other like the finger prints of the human beings.

Further, it will be discussed later that the line spectra are obtained as a result of absorption and subsequent emission of energy by the electrons in the individual atoms of the element. Hence the line spectrum is also called atomic spectrum.

2. Absorption spectra When white light from any source is first passed through the solution or vapours of a chemical substance and then analysed by the spectroscope, it is observed that some dark lines are obtained in the otherwise continuous spectrum (Figure). These dark lines are supposed to result from the fact that when white light (containing radiations of many wavelengths) is passed through the chemical substance, radiations of certain wavelengths are absorbed, depending upon the nature of the element. Further it is observed that the dark lines are at the same place where coloured lines are obtained in the emission spectra for the same substance. This shows that the wavelengths absorbed were same as were emitted in the emission spectra. The spectrum thus obtained is, therefore, called ‘absorption spectrum’.

Emission spectrum of Hydrogen When hydrogen gas at low pressure is taken in the discharge tube and the light emitted on passing electric discharge is examined with a spectroscope, the spectrum of hydrogen (Fig. b). It is found to consist of a large number of lines which are grouped into different series, named after the discoverers. The names of these series and the regions in which they are found to lie are given in the Figure below.

Dual Nature of Matter and Radiation.

In case of light, some phenomena like interference, diffraction etc. can be explained if the light is supposed to have wave character. However, certain other phenomena such as black body radiation and photoelectric effect can be explained only if it is believed to be a stream of photons i.e., has particle character (or is corpuscular iature). Thus, light is said to have a dual character. Such studies on light were made by Einsterin in 1905.

Louis de Broglie, a French physicist, in 1924, advanced the idea that like photons, all material particles such as electron, proton, atom, molecule, a piece of chalk, a piece of stone or an iron ball (i.e. microscopic as well as macroscopic objects) possessed both wave character as well as particle character. The wave associated with a particle is called a matter wave.

The de Broglie Relation. The wavelength of the wave associated with any material particle was calculated by analogy with photon as follows:– In case of a photon, if it is assumed to have wave character, its energy is given by

de Broglie pointed out that the above equation is applicable to any material particle. The mass of the photon is replaced by the mass of the material particle and the velocity c of the photon is replaced by the velocityof the material particle. Thus, for any material particle like electron, we may write.

Thus the significance of de Broglie equation lies in the fact that it relates the particle character with the wave character of matter.

Distinction between a particle and a wave. The concept of a particle and a wave can be under-stood by the different points of distinction between them given in table 1.

Table Points of distinction between a particle and a wave

Characteristics of Matter waves and Electromagnetic waves. Matter waves differ from electromagnetic waves in the various respects given in table 2 oext page.

Significance of de Broglie equation. Although the de Broglie equation is applicable to all material objects but it has significance only in case of micro-scopic particles. This will be clear from the following example:

Table Difference between electromagnetic waves and matter waves

Consider a ball of mass 0.1 kg moving with a speed of 60 m s^-1. From de Broglie equation, the wavelength of the associated wave is or approx. 10^-34 m. It is apparent that this wavelength is too small for ordinary observation. On the other hand, an electron with a rest mass equal to 9.11 × 10^-31 kg i.e. approx. 10^-30 kg moving at the same speed would have a wavelength m i.e. 105 Å which can be easily measured experimentally.

Since we come across macroscopic objects in our everyday life, therefore de Broglie relationship has no significance in everyday life. That is why we do not observe any wave nature associated with the motion of a running car or a cricket ball etc.

Experimental verification of the dual character of electrons.

(a) Verification of wave character.

(i) Davisson and Germer’s experiment. Davisson and Germer in 1927 observed that when a beam of electrons is allowed to fall on the surface of a nickel crystal and the scattered or the reflected rays are received on a photographic plate, a diffraction pattern (consisting of a number of concentric rings), similar to that produced by X-rays, is obtained. Now, since X-rays are electromagnetic waves i.e., they are confirmed to have wave character, therefore, electrons must also have wave character. Moreover, the wavelength determined from the diffraction is found to be very nearly the same as calculated from de Broglie equation. This furhter lent support to de Broglie equation.

(ii) Thomson’s experiment. G.P. Thomson in 1928 performed experiments with thin foil of gold in place of nickel crystal. He observed that if the beam of electrons after passing through the thin foil of gold is received on the photographic plate placed perpendicular to the direction of the beam, a diffraction pattern is observed as before. This again confirmed the wave nature of electrons.

(b) Verification of the particle character. The particle character of the electron is proved by the following different experiments :

·       When an electron strikes a zinc sulphide screen, a spot of light known as scintillation is produced. Since a scintillation is localized on the zinc sulphide screen, therefore the striking electron which produces it also must be localized and is not spread out on the screen. But the localized character is possessed by particles (as already explained on page below). Hence electron has particle character.

·                   Experiments such as Thomson’s experiment for determination of the ratio of charge to mass (i.e. e/m) and Milliken oil drop experiment for determination of charge on electron also show that electron has particle character.

·                   The phenomenon of Black body radiation and Photoelectric effect also prove the particle nature of radiation. The most important application of de Broglie concept is in the construction of electron microscope which is used in the measurement of size of very small objects.

Derivation of Bohr’s postulate of angular momentum from de Broglie equation. According to Bohr’s model, the electron revolves around the nucleus in circular orbits. According to de Broglie concept, the electron is not only a particle but has a wave character. Thus in order that the wave may be completely in phase the circumference of the orbit must be equal to an integral multiple of wavelength i.e.,

Heisenberg’s Uncertainty Principle

All moving objects that we see around us e.g. a car, a planet, a ball thrown in the air etc move along definite paths or trajectories. Hence their position and velocity can be measured accurately at any instant of time. However, such an accurate measurement is not possible for sub-atomic particles.

As a consequence of dual nature of matter, Werner Heisenberg, a German physicist, in 1927 gave a principle about the uncertainties in simultaneous measurements of position and momentum of small particles. It is known as Heisenberg’s uncertainty principle and it states as follows : It is impossible to measure simultaneously the position and momentum of a small particle with absolute accuracy or certainty. If an attempt is made to measure any one of these two quantities with higher accuracy, the other becomes less accurate. The product of the uncertainty in the position (x) and the uncertainty in the momentum (p = m. where m is the mass of the particle and is the uncertainty in velocity) is always constant and is equal to or greater than h/4, where h is Planck’s constant i.e.,

x . p>=h/4 …(i)

Explanation of Heisenberg’s uncertainty principle. The basis for the above principle may be understood from the following description :

Suppose we attempt to measure both the position and momentum of an electron. To pin-point the position of the electron, we have to use light so that the photon of light strikes the electron and the reflected photon is seen in the microscope. As a result of the hitting, the position as well as the velocity of the electron are disturbed.

But according to principle of optics, the accuracy with which the position of a particle can be measured depends upon the wavelength of light used. The uncertaintly in position is ±. The shorter the wavelength, the greater is the accuracy. But shorter wavelength means higher frequency and hence higher energy. This high energy photon on striking the electron changes its speed as well as direction.

Alternatively, shorter wavelength implies higher momentum (as = h/p i.e. p = h/). Thus photon will have higher momentum and a larger but indefinite amount of it will be transferred to the electron at the time of collision. This will result in greater uncertainty in the velocity of the electron. On the other hand, decreasing the momentum means increasing the wavelength which will lead to greater uncertainty in position.

Significance of Heisenberg’s uncertainty principle. Like de Broglie equation, although Heisenberg’s uncertainty principle holds good for all objects but it is of significance only for microscopic particles. The reason for this is quite obvious. The energy of the photon is insufficient to change the position an velocity of bigger bodies when it collides with them. For example, the light from a torch falling on a running rat in a dark room neither changes the speed of the rat nor its direction i.e. position. Since in everyday life, we come across big objects only, the position and velocity of which can be measured accurately, Heisenberg’s uncertainty principle has no significance in everyday life.

Why electron cannot exist in the nucleus? On the basis of Heisenberg’s uncertainty principle, it can be shown why electrons cannot exist within the atomic nucleus. This is because the diameter of the atomic nucleus is of the order of 10^-14 m. Hence if the dlectron were to exist within the nucleus, the maximum uncertainty in its position would have been 10^-14 m. Taking the mass of electron as 9.1 × 10^-31 kg, the minimum uncertainty in velocity can be calculated by applying uncertainty principle. This value is much higher than the velocity of light (viz 3 × 108 ms–1) and hence is not possible.

 

BLACK BODY RADIATION AND PHOTOELECTRI EFFECT

Black body radiation. If any substance with high melting point (e.g, an iron bar) is heated, it first becomes red, then yellow and finally begins to glow with white light.

If the substance beings heated is a black body (which is a perfect absorber and perfect radiator of energy) the radiation emitted is called black body radiation. According to electromagnetic wave theory, the energy is emitted or absorbed continuously. Hence, the energy of any electromagnetic radiation is proportional to its intensity i.e. a square of amplitude and is independent of its frequency or wavelength. Thus, according to the wave theory, the radiation emitted by the body being heated should have the same colour, although its intensity may vary as the heating is continued.

Photoelectric effect. When radiations with certain minimum frequency () strike the surface of a metal, the electrons are ejected from the surface of the metal (Figure). This phenomenon is called photoelectric effect. The electrons emitted are called photo-electrons.

However, the following three important facts are obwerved about the photoelectric effect :

(i) The electrons are ejected only if the radiation striking the surface of the metal has at least a minimum frequency. If the frequency is less than , electrons are ejected. This value  is called Threshold Frequency.

(ii) The velocity (and hence the kinetic energy) of the electron ejected depends upon the frequency of the incident radiation and is independent of its intensity.

(iii) The number of photoelectrons ejected is proportional to the intensity of incident radiation.

The above observations cannot be explained by the Electromagnetic wave theory. According to this theory, since radiations are continuous, therefore it should be possible to accumulate energy on the surface of the metal, irrespective of its frequency and thus radiations of all frequencies should be able to eject electrons.

Similarly, according to this theory, the energy of the electrons ejected should depend upon the intensity of the incident radiation.

Planck’s Quantum Theory. To explain the phenomena of ‘Black body radiation’ and ‘Photoelectric effect,’ Max Planck is 1900, put forward a theory known after his name as Planck’s quantum theory. This theory was further extended by Einstein in 1905. The main points of this theory are as follows:

(i) The radiant energy is emitted or absorbed not continuously but discontinuously in the form of small discrete packets of energy, Each such packet of energy is called a ‘quantum’. In case of light, the quantum of energy is called a ‘photon’.

(ii) The energy of each quantum is directly proportional to the frequency of the radiation i.e.,

(iii) The total amount of energy emitted or absorbed by a body will be some whole number quanta. Hence whereis any integer.

Explanation of Black Body Radiation. When some solid substance is heated, the atoms of the substance are set into oscillation and emit radiation of frequency, . Now, as heating is continued, more and more energy is being absorbed by the atoms and they emit radiations of higher and higher frequency. As red light has minimum frequency, yellow has higher frequency, therefore, the body on heating becomes first red, then yellow and so on.

Explanation of Photoelectric effect. Planck’s quantum theory gives an explanation of the different points of the photoelectric effect as under :

(i) When light of some particular frequency falls on the surface of metal, the photon gives its entire energy to the electron of the metal atom. The electron will be dislodged or detached from the metal atom only if the energy of the photon is sufficient to overcome the force of attraction of the electron by the nucleus. That is why photo-electrons are ejected only when the incident light has a certain minimum frequency (threshold frequency ).

(ii) If the frequency of the incident light () is more than the threshold frequency (), the excess energy is imparted to the electron as kinetic energy. i.e. K.E. of the ejected electron =. Hence greater is the frequency of the incident light, greater is the kinetic energy of the emitted electron.

(iii) Increasing the intensity of light of a given frequency increases the number of photons but does not increase the energies of photons. Hence, when the intensity of light is increased, more electrons are ejected but the energies of these electrons are not altered.

Thus, in the visible light, as violet radiations have maximum frequency and the red radiations have minimum frequency violet light has more energy than the red light. Similarly, the ultraviolet light has higher energy than the violet light and the infrared light has less energy than even the red light.

If kinetic energy of the emitted photo-electrons is plotted against the frequency of the absorbed photons, a straight line of slope h is obtained (Figure).

Stopping potential ; The minimum potential at which the plate photoelectric current becomes zero is called stopping potential. If is the stopping potential, then

Theories of Nuclear Stability

Since a nucleus contains positively charged protons, there must exist a strong repulsive force between them. It has been calculated that there exists an electrostatic repulsion of approximately six tons between two protons situated at a nuclear distance but at the same time the forces which bind the nucleus are very high. It has been found that nuclear forces attracting the same two particles (i.e., protons) are at least forty times greater than the repuslive forces. Thus, two major forces exist in the nucleus. These are electrostatic and nuclear. The nuclear forces are stronger and the range of these forces is extremely small. The forces which operate betweeucleons are referred to as exchange forces. In order to account for the stability of the nucleus, a theory known as meson theory was put forward by Yukawa, in 1935. Yukawa pointed out that neutrons and protons are held together by very rapid exchange of nuclear particles called pi mesons. These mesons may be electrically neutral, positive or negative and possess a mass 275 times the mass of an electron. Nuclear forces arise from a constant exchange of mesons betweeucleons with very high velocity (practically the velocity of light).

Let a neutron be converted into a proton by the emission of a negative meson. The emitted meson is accepted by another proton and converted into a neutron.

Similarly, a proton after emitting a positive meson is converted into a neutron and vice-versa.

There may be two more types of exchange, i.e., betweeeutron-neutron and proton-proton, involving neutral pi mesons.

Mass defect—Binding energy.

It is observed that the atomic mass of all nuclei (except hydrogen) is different from the sum of the masses of protons and neutrons. For example, the helium nucleus consists of 2 protons and 2 neutrons. The combined mass of 2 protons and 2 neutrons should be

= 2 × 1.00758 + 2 × 1.00893 = 4.03302 amu

The actual observed mass of helium nuclei is 4.0028 amu. A difference of 0.0302 amu is observed between these two values. This difference is termed as
mass defect.

Mass defect = Total mass of nucleons – observed atomic mass

This decrease in mass (i.e., mass defect) is converted into energy according to Einstein equation E = mc². The energy released when a nucleus is formed from protons and neutrons is called the binding energy. This is the force which holds all the nucleons together in the nucleus. Binding energy can be defined in other ways also, i.e., the energy required to break the nucleus into constituent protons and neutrons. Binding energy is measured in MeV (million electron-volts), i.e., 1 amu = 931 MeV.

Binding energy = Mass defect × 931 MeV

Binding energy can also be calculated in ergs. This is: = Mass defect (amu) × 1.66 × 10–24 × (3 ×1010)2 erg [1 MeV = 1.60 × 106 erg]

The binding energy increases with the increase in atomic number of the element. This indicates that heavier nuclei should be more stable than lighter nuclei. But, it is not so because heavier nuclei above atomic number 82 are unstable. It is thus clear that total binding energy of a nucleus does not explain the stability of the nucleus.

The total binding energy of a nucleus when divided by the number of nucleons gives the average or mean binding energy per nucleon. The binding energy per nucleon is actually the measure of the stability of the nucleus. The greater the binding energy per nucleon, more stable is the nucleus.

When binding energy per nucleon of a number of nuclei is plotted against the corresponding mass number, a graph is obtained (Figure) whose characteristics are as follows:

Bohr’s theory of the atomic spectrum of Hydrogen

In 1913, Niels Bohr combined elements of quantum theory and classical physics in a treatment of the hydrogen atom. He stated two postulates for an electron in an atom: Stationary states exist in which the energy of the electron is constant; such states are characterized by circular orbits about the nucleus in which the electron has an angular momentum mvr given by equation. The integer, n, is the principal quantum number.

Energy is absorbed or emitted only when an electronmoves fromone stationary state to another and the energy change is given by equation 1.7 where n1 and n₂ are the principal quantum numbers referring to the energy levels En₁ and En₂ respectively.

If we apply the Bohr model to the H atom, the radius of each allowed circular orbit can be determined from equation 1.8. The origin of this expression lies in the centrifugal force acting on the electron as it moves in its circular orbit; for

the orbit to be maintained, the centrifugal force must equal the force of attraction between the negatively charged electron and the positively charged nucleus.

From equation 1.8, substitution of n= 1 gives a radius for the first orbit of the H atom of 5,293*10^–11 m, or 52.93 pm. This value is called the Bohr radius of the H atom and is given the symbol a₀. An increase in the principal quantum number from n=1 to n=∞ has a special significance; it corresponds to the ionization of the atom and the ionization energy, IE. Values of IEs are quoted per mole of atoms:

One mole of a substance contains the Avogadro number, L, of particles:

L = 6,022*10²³ mol ^-1

Although the SI unit of energy is the joule, ionization energies are often expressed in electron volts (eV) (1 eV =96,4853 ≈ 96,5 kJ mol^-1). Impressive as the success of the Bohr model was when applied to the H atom, extensive modifications were required to cope with species containing more than one electron; we shall not pursue this further here.

 (i) Binding energy per nucleon increases from 1.1 to 8.0 MeV from mass number 2 to 20.

(ii) Binding energy per nucleon increses from 8 to 8.6 MeV from mass number 20 to 40.

(iii) Binding energy per nucleon remains 8.6 – 8.7 MeV from mass number 40 to 90. Iron (56) has the maximum value of 8.7 MeV per nucleon.

(iv) The value of binding energy per nucleon decreases from 8.6 to 7.5 MeV from mass number 90 to 240.

(v) Points for helium, carbon, oxygen lie quite high in the graph showing that these nuclei are highly stable.

The binding energy per nucleon can be increased in two ways:

(i) Either by breaking heavy nucleus to those of intermediate mass numbers (process of fission) or

(ii) By fusing lighter nuclei to form heavier nuclei (process of fusion).

The Schrodinger wave equation

where m=mass, E= total energy and V = potential energy of the particle.

Information about the wavefunction is obtained from the Schrodinger wave equation, which can be set up and solved either exactly or approximately; the Schro. dinger equation can be solved exactly only for a species containing a nucleus and only one electron, i.e. a hydrogen-like system. Of course, in reality, electrons move in three-dimensional space and an appropriate form of the Schrodinger wave equation is given in equation.

3. Quantum numbers. Aufbau principle (Hund’s rules and the Pauli exclusion principle)

An atom contains a large number of orbitals. These are distinguished from each other on the basis of their size, shape and orientation (direction) in space. These parameters of an orbital are expressed in terms of three numbers, called principal, azimuthal and magnetic quantum numbers. Further to represent the spin (rotation) of the electron about its own axis, a fourth quantum number, called spin quantum number is introduced.

These numbers are like the postal address of a person. To know about a particular person, Mr X, we should know about his country, his town, his lane and house number.

The various quantum numbers are briefly described below :

1. Principal Quantum Number. It is represented by ‘n’. It gives the following information :

(i) Approximate distance of the electron from the nucleus i.e. the size of the electron cloud.

(ii) Energy of the electron present in any shell*, e.g. for hydrogen atom,

(iii) Maximum number of electrons present in any shell (given by the formula 2n2).

This number helps to explain the main lines of the spectrum.

It can have values= 1, 2, 3, 4……..etc. which are called K, L, M, N…….etc. shells respectively.

2. Azimuthal (or Subsidiary or Angular momentum) Quantum Number. This number is represented by ‘l’. It is found that the energy of an electron calculated from the value ofincludes in itself some contribution due to angular momentum of the electron. As different electrons may have different angular momenta, the electrons within the same shell occupy different energy levels called sub-levels or sub-shells. The azimuthal quantum number gives the following information:

(i) Number of sub-shells present within any main shell

(ii) Contribution of energy due to angular momentum towards the total energy of the electron.

(iii) Relative energies of the sub-shells belonging to the same shell.

(iv) Shapes of the subshells.

(v) Orbital angular momentum.

This number helps to explain the fine lines of the spectrum because due to the presence of a large number of sub-levels, the number of probable transitions (jumps) of electrons becomes very large.

For a given value of n, l can have values from 0 to– 1.

For example,

For= 1, l = 0 i.e. only one value

For= 2, l = 0, 1 i.e. two values

For= 3, l = 0, 1, 2, i.e. four values

For= 4, l = 0, 1, 2, 3, i.e. four values

Thus 1st, 2nd, 3rd, 4th shells have 1, 2, 3, and 4 sub-shells respectively. In general, nth shell hassub-shells.

Further, these sub-shells are designated by the letters s, p, d and f for l = 0, 1, 2, and 3 respectively (derived from the first letter of the words sharp, principal, diffused and fundamental lines of the spectra)

(The prefix before the symbol of sub-shell represents value of n).

The energies of the different sub-shells present within the same main shell are found to be in the order s < p < d < f

Further the electron cloud of ‘s’ is found to be spherical while that of ‘p’ is found to be dumb-bell shaped. d and f have complex shapes.

3. Magnetic Quantum Number. This number is represented by ‘m’. This number is required to explain the fact that when the source giving the line spectrum is placed in a magnetic field, each spectral line splits into a number of lines (Zeeman effect). This was obviously due to the fact that each subshell contains a number of orbitals which take up different orientations under the influence of the external magnetic field. The magnetic quantum number tells the number of orientations which the orbitals present within the same sub-shell can take up. In other words, it tells the number of orbitals present within the same sub-shell (as each orientation represents an orbital).

For a given value of l, m can have values from – l to + l including ‘0’.

For s-sub-shell, l = 1. Hence m = – 1, 0, + 1 (three values) i.e. p-sub-shell has three orbitals oriented along X-axis, Y-axis and Z-axis and represented by p_x, p_y and p_z respectively*.

Similarly, for d-sub-shell, l = 2 so that m = – 2, – 1, 0, +1, +2 i.e. d-sub-shells contain five orbitals. For f-sub-shell, l = 3 so that m = – 3, – 2, – 1, 0, + 1, + 2, + 3 i.e. f-sub-shell has seven orbitals.

Different values of ‘m’ for a given value of ‘l’ provide the total number of ways in which a given s,p,d,f subshell in presence of magnetic field can be arranged in space along x,y and z axes or total number of orbitals into which a given subshell can be divided.

When l = 0, m = 0, i.e., one value implies that ‘s’ subshell has only one space orientation and hence, it can be arranged in space only in one way along x, yor z axes. Thus, ‘s’ orbital has a symmetrical spherical shape and is usually represented as in Figure below.

In case of 1s orbital the electron cloud is maximum at the nucleus and decreases with the distance. The electron density at a particular distance is uniform in all directions. The region of maximum electron density is called antinode. In case of ‘2s’ orbital, the electron density is again maximum at the nucleus and decreases with increase in distance. The ‘2s’ orbital differs in detail from a 1s orbital. The electron in a ‘2s’ orbital is likely to be found in two regions, one near the cucleus and other in a spherical shell about the nucleus. Electron density is zero in nodal region

When l = 1, ‘m’ has three values –1, 0, + 1. It implies that ‘p’ subshell of any energy shell has three space orientations, i.e., three orbitals. Each p-orbital has dumb-bell shape. Each one is disposed symmetrically along one of the three axes as shown in figure below. p-orbitals have directional character.

When l = 2, ‘m’ has five values –2, –1, 0, + 1, + 2. It implies that d-subshell of any energy shell has five orientations, i.e., five orbitals. All the five orbitals are not identical in shape. Four of the d-orbitals d_xy, d_yz, d_zx, contain four lobes while fifth orbital consists of only two lobes. The lobes of orbital lie between x and y axes. Similar is the case for and . Four lobes of orbital are lying along x and y axes while the two lobes of orbital are lying along z axes and contain a ring of negative charge surrounding the nucleus in xy plane figure below.

There are seven f-orbitals designated as Their shapes are complicated ones.

Spherical nodes and nodal planes

(a)       Spherical node. The spherical surface where the probability of finding an electron is zero is called a spherical node. In general, number of spherical nodes in an orbital =– l – 1, where n is the principal quantum number and l is the azimuthal quantum number.

For example,

(i) For 1s, n = 1 and l = 0

No. of spherical nodes = 1 – 0 – 1 = 0

(ii) For 2s, n = 2 and l = 0

No. of spherical nodes = 2 – 0 – 1 = 1

(iii) For 2p, n = 2 and l = 1

No. of spherical nodes = 2 – 1 – 1 = 0

(iv) For 3s, n = 3 and l = 0

No. of spherical nodes = 3 – 0 – 1 = 2

(iv) For 3p, n = 3 and l = 1

No. of spherical nodes = 3 – 1 – 1 = 1

b) Nodal planes. The planes in which the probability of finding an electron is zero is called a nodal plane. Number of nodal planes for an orbital = l. For example, (i) s-orbital (l = 0) has no nodal plane (ii) p-orbital (l = 1) has one nodal plane (iii) d-orbital (l = 2) has two nodal planes (iv) f-orbital (l = 3) has three nodal planes.

1. The designation of the seven f-orbitals are .

2. In the plots of radial probability versus distance from nucleus, number of peaks i.e. regions of maximum probability = n – l (No. of radial nodes =– l – 1 as already explained in the text).

3. The reason why 4s orbital has lesser energy than 3d orbital is that 4s-orbital has three small peaks closer to the nucleus (in addition to the 4th high peak). Thus 4s is more penetrating than 3d i.e. held more tightly to the nucleus and hence has lower energy.

4. The opposite lobes of p-orbitals have different signs (one +ve, the other –ve) but opposite lobes of d-orbitals have the same sign (two lobes have +ve sign while the other two have –ve sign).

4. Spin Quantum Number. It is represented by ‘s’. This number was introduced to account for the fact that the electron in an atom not only moves around the nucleus but also spins about its own axis (like the earth which not only revolves around the sun but also spins around its own axis). This number gives the information about the direction of spin-ning of the electron present in any orbital. Since the electron in an orbital can spin either in the clock-wise direction or in the anti-clockwise direction, hence for a given value of m, s can have only two values i.e. + 1/2 and – 1/2 or these are very often represented by two arrows pointing in the opposite direction i.e.

This quantum number helps to explain the magnetic properties of the substances. A spinning electron behaves like a micromagnet with a definite magnetic moment. If an orbital contains two electrons, the two magnetic moments oppose and cancel each other.

Thus in an atom, if all the orbitals are fully filled, net magnetic moment is zero and the sub-stance is diamagnetic (i.e. repelled by the external magnetic field). However, if some half-filled orbitals are present, the substance has a net magnetic moment and is paramagnetic (i.e. attracted by the external magnetic field).

Filling Of Orbitals Atoms

The filling of electrons into the orbitals of different atoms takes place according to the following three rules :

(1) Aufbau Principle. The word ‘aufbau’ in German means ‘building up’. The building up of orbitals means the filling up of orbitals with electrons. The principle states as follows :

 

The order in which the energies of the orbitals increase and hence the order in which the orbitals are filled is as follows:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p…..

This order may be remembered by using the method given in Figure below. Starting from the top, the direction of the arrows gives the order of filling of orbitals.

Alternatively, the order of increase of energy of orbitals can be calculated from (n + l) rule, explained in the next column.

The energy of an orbitals depends upon the values of principal quantum number,and the azimuthal quantum number l (in the absence of an external magnetic field). The (n + l) rule states as follows :

 

The following table illustrates the (n +l) rule:

It may be noted that different subshells of a particular shell have different energies only in case of multi-electron atoms.

(2) Pauli Exclusion Principle.

As already explained, Pauli exclusion principle states as follows:

If an orbital is represented by a circle and it contains two electrons (i.e. the two arrows must point in the opposite direction. The electrons are said to be paired or the orbitals is said to be fully filled.

The electron is said to be in an unpaired state.

(3) Hund’s Rule of Maximum Multiplicity. This rule deals with the filling of electrons into the orbitals belonging to the same sub-shell (i.e. orbitals of equal energy, called degenerate orbitals). It states as under :

Since there are three p, five d and seven f orbitals, therefore the pairing of electrons will start in the p, d and f orbitals with the entry of 4th, 6th and 8th electron respectively. Since there are three p, five d and seven f orbitals, therefore the pairing of electrons will start in the p, d and f orbitals with the entry of 4th, 6th and 8th electron respectively. The reason for such a tendency in quite obvious. The electrons are negatively charged and repel each other. Hence they spread out and occupy the identical orbitals singly before they begin to pair. As a result, the repulsions are minimum. Hence the energy is minimum and the stability is maximum. Pairing occurs because less energy is needed to do so than the energy required to place the electron in the next higher empty orbital. Further it is important to note that whenever orbitals are singly occupied as above, the electrons present in them have the spin in the same direction i.e. either all clockwise or all anticlockwise. This is because of the fact that such a state has lower energy and hence is more stable.

Electronic Configuration of Atoms

Keeping in view the above rules, and representing an orbital by a circle and an electron and the direction of its spin by an arrow.

The above method of writing the electronic configurations is quite cumbersome. Hence, usually the electronic configuration of the atom of any element is simply represented by the notation.

 

e.g. 1s² means 2 electrons are present in the s-subshell of the 1st main shell.

To get the complete configuration of an atom, a number of such notations are written one after the other in order of increasing energies of the orbitals, starting always with the orbital of lowest energy i.e. 1s. Using the above method of representation, the electronic configurations of the various elements are listed in table below.

Some exceptional electronic configurations.

Some elements such as chromium (At. No. 24), copper (At. No. 29) etc. possess electronic configurations different from those expected from the aufbau order. This is because of the tendency of the sub-shells to be exactly half-filled or completely filled.

 

Thus generally only one electron jumps from lower energy orbital to higher energy orbital e.g. from 4s to 3d. However in case of palladium, two electrons are involved (the only case with a difference. The reason for the tendency of the subshells to be completely filled or exactly half-filled is that it leads to greater stability.

Cause of greater stability of exactly half-filled and completely filled configurations.  The greater stability of these configurations is due to the following two reasons :

(i) Symmetry.

The half-filled and completely filled configurations are more symmetrical and symmetry leads to greater stability.

(ii) Exchange energy.

The electrons present in the different orbitals of the same subshell can exchange their positions. Each such exchange leads to a greater stability which can be explained in terms of exchange energy. As the number of exchanges that can take place is maximum in the exactly half-filled and completely filled arrangements (i.e. more in d⁵ than in d⁴ and more in d¹⁰ than in d⁹ ), therefore exchange energy is maximum and hence the stability is maximum.

Some important points in writing electronic configurations.

While writing the electronic configurations, the following points may also be noted:

(i) To avoid the writing of electronic configurations in a lengthy way, usually the symbols [He]² , [Ne]¹⁰ , [Ar]¹⁸ etc. are used as the first part of the configuration. Such a symbol stands for the electronic configuration of that inert gas and is usually called the core of the inert gas.

(ii) Although the orbitals of lower energy are filled first but the electronic configuration are writteot in the order in which the orbitals were filled but in the order of principal quantum numbers.

(iii) Unless otherwise mentioned, electronic configuration always means the electronic configuration in the ground state.

(iv) Always remember that if you write down electronic configuration of ion (cation or anion), than first you write configuration of basic atom than add or remove the electron from the system otherwise always there is a chance of error.

For example

For elements with very high atomic numbers, some deviations are observed other than on account of half-filled and fully filled subshells. However, for our purposes, such exceptions are not important.

Table. Electronic configuration of elements in the ground state

4. The periodic law of Mendeleev D.I. and it modern interpretation. Structure of the periodic system. Type of the periodic system. Periodic properties of elements.

In 1869 and 1870 respectively, Dmitri Mendeleev and Lothar Meyer stated that the properties of the elements can be represented as periodic functions of their atomic weights, and set out their ideas in the form of a periodic table.

The modern periodic table in which the elements are arranged iumerical order according to the number of protons (and electrons) they possess. The division into groups places elements with the same number of valence electrons into vertical columns within the table. The groups are labelled from 1 to 18 (Arabic numbers). The vertical groups of three d-block elements are called triads. Rows in the periodic table are called periods. The first period contains H and He, but the row from Li to Ne is sometimes referred to as the first period. Strictly, the lanthanoids include the 14 elements Ce–Lu, and the actinoids include Th–Lr; however, common usage places La with the lanthanoids, and Ac with the actinoids.

A modern periodic table emphasizes the blocks of 2, 6, 10 and 14 elements which result from the filling of the s, p, d and f atomic orbitals respectively.

Recommended names for groups of elements in the periodic table.

Note the distinction between a transition and d-block element. Elements in groups 3–12 inclusive are collectively called d-block elements, but by the IUPAC rulings, a transition metal is an element, an atom of which possesses an incomplete d-shell or which gives rise to a cation with an incomplete d-shell. Thus, elements in group 12 are not classed as transition elements.

The layout of the periodic table demonstrates recurring (“periodic”) chemical properties. Elements are listed in order of increasing atomic number (i.e., the number of protons in the atomic nucleus). Rows are arranged so that elements with similar properties fall into the same columns (groups or families). According to quantum mechanical theories of electron configuration within atoms, each row (period) in the table corresponded to the filling of a quantum shell of electrons. There are progressively longer periods further down the table, grouping the elements into s-, p-, d- and f-blocks to reflect their electron configuration.

In printed tables, each element is usually listed with its element symbol and atomic number; many versions of the table also list the element’s atomic mass and other information, such as its abbreviated electron configuration, electronegativity and most common valence numbers.

As of 2010, the table contains 118 chemical elements whose discoveries have been confirmed. Ninety-four are found naturally on Earth, and the rest are synthetic elements that have been produced artificially in particle accelerators. Elements 43 (technetium), 61 (promethium) and all elements greater than 83 (bismuth), beginning with 84 (polonium) have no stable isotopes. The atomic mass of each of these element’s isotope having the longest half-life is typically reported on periodic tables with parentheses. Isotopes of elements 43, 61, 93 (neptunium) and 94 (plutonium), first discovered synthetically, have since been discovered in trace amounts on Earth as products of natural radioactive decay processes. The primary determinant of an element’s chemical properties is its electron configuration, particularly the valence shell electrons. For instance, any atoms with four valence electrons occupying p orbitals will exhibit some similarity. The type of orbital in which the atom’s outermost electrons reside determines the “block” to which it belongs. The number of valence shell electrons determines the family, or group, to which the element belongs.

The total number of electron shells an atom has determines the period to which it belongs. Each shell is divided into different subshells, which as atomic number increases are filled in roughly this order (the Aufbau principle) (see table). Hence the structure of the table. Since the outermost electrons determine chemical properties, those with the same number of valence electrons are grouped together. Progressing through a group from lightest element to heaviest element, the outer-shell electrons (those most readily accessible for participation in chemical reactions) are all in the same type of orbital, with a similar shape, but with increasingly higher energy and average distance from the nucleus. For instance, the outer-shell (or “valence”) electrons of the first group, headed by hydrogen, all have one electron in an s orbital. In hydrogen, that s orbital is in the lowest possible energy state of any atom, the first-shell orbital (and represented by hydrogen’s position in the first period of the table). In francium, the heaviest element of the group, the outer-shell electron is in the seventh-shell orbital, significantly further out on average from the nucleus than those electrons filling all the shells below it in energy. As another example, both carbon and lead have four electrons in their outer shell orbitals. Note that as atomic number (i.e., charge on the atomic nucleus) increases, this leads to greater spin-orbit coupling between the nucleus and the electrons, reducing the validity of the quantum mechanical orbital approximation model, which considers each atomic orbital as a separate entity. The elements ununtrium, ununquadium, ununpentium, etc. are elements that have been discovered, but so far have not received a trivial name yet. There is a system for naming them temporarily.

5. The mechanism of formation of chemical bonds. The types of chemical bonds, it property.

A chemical bond is an attraction between atoms or molecules that allows the formation of chemical compounds, which contain two or more atoms. A chemical bond is the attraction caused by the electromagnetic force between opposing charges, either between electrons and nuclei, or as the result of a dipole attraction. The strength of bonds varies considerably; there are “strong bonds” such as covalent or ionic bonds and “weak bonds” such as dipole-dipole interactions, the London dispersion force and hydrogen bonding. Since opposite charges attract via a simple electromagnetic force, the negatively charged electrons orbiting the nucleus and the positively charged protons in the nucleus attract each other. Also, an electron positioned between two nuclei will be attracted to both of them. Thus, the most stable configuration of nuclei and electrons is one in which the electrons spend more time between nuclei, than anywhere else in space. These electrons cause the nuclei to be attracted to each other, and this attraction results in the bond. However, this assembly cannot collapse to a size dictated by the volumes of these individual particles. Due to the matter wave nature of electrons and their smaller mass, they occupy a very much larger amount of volume compared with the nuclei, and this volume occupied by the electrons keeps the atomic nuclei relatively far apart, as compared with the size of the nuclei themselves. In general, strong chemical bonding is associated with the sharing or transfer of electrons between the participating atoms. Molecules, crystals, and diatomic gases— indeed most of the physical environment around us— are held together by chemical bonds, which dictate the structure of matter.

In the simplest view of a so-called covalent bond, one or more electrons (often a pair of electrons) are drawn into the space between the two atomic nuclei. Here the negatively charged electrons are attracted to the positive charges of both nuclei, instead of just their own. This overcomes the repulsion between the two positively charged nuclei of the two atoms, and so this overwhelming attraction holds the two nuclei in a fixed configuration of equilibrium, even though they will still vibrate at equilibrium position. In summary, covalent bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared. In a polar covalent bond, one or more electrons are unequally shared between two nuclei.

In a simplified view of an ionic bond, the bonding electron is not shared at all, but transferred. In this type of bond, the outer atomic orbital of one atom has a vacancy which allows addition of one or more electrons. These newly added electrons potentially occupy a lower energy-state (effectively closer to more nuclear charge) than they experience in a different atom. Thus, one nucleus offers a more tightly bound position to an electron than does another nucleus, with the result that one atom may transfer an electron to the other. This transfer causes one atom to assume a net positive charge, and the other to assume a net negative charge. The bond then results from electrostatic attraction between atoms, and the atoms become positive or negatively charged ions.

All bonds can be explained by quantum theory, but, in practice, simplification rules allow chemists to predict the strength, directionality, and polarity of bonds. The octet rule and VSEPR theory are two examples. More sophisticated theories are valence bond theory which includes orbital hybridization and resonance, and the linear combination of atomic orbitals molecular orbital method which includes ligand field theory. Electrostatics are used to describe bond polarities and the effects they have on chemical substances.

Early speculations into the nature of the chemical bond, from as early as the 12th century, supposed that certain types of chemical species were joined by a type of chemical affinity. In 1704, Isaac Newton famously outlined his atomic bonding theory, in “Query 31” of his Opticks, whereby atoms attach to each other by some “force”. Specifically, after acknowledging the various popular theories in vogue at the time, of how atoms were reasoned to attach to each other, i.e. “hooked atoms”, “glued together by rest”, or “stuck together by conspiring motions”, Newton states that he would rather infer from their cohesion, that “particles attract one another by some force, which in immediate contact is exceedingly strong, at small distances performs the chemical operations, and reaches not far from the particles with any sensible effect.”

In 1819, on the heels of the invention of the voltaic pile, Jöns Jakob Berzelius developed a theory of chemical combination stressing the electronegative and electropositive character of the combining atoms. By the mid 19th century, Edward Frankland, F.A. Kekule, A.S. Couper, A.M. Butlerov, and Hermann Kolbe, building on the theory of radicals, developed the theory of valency, originally called “combining power”, in which compounds were joined owing to an attraction of positive and negative poles. In 1916, chemist Gilbert N. Lewis developed the concept of the electron-pair bond, in which two atoms may share one to six electrons, thus forming the single electron bond, a single bond, a double bond, or a triple bond; in Lewis’s own words, “An electron may form a part of the shell of two different atoms and cannot be said to belong to either one exclusively.”

That same year, Walther Kossel put forward a theory similar to Lewis’ only his model assumed complete transfers of electrons between atoms, and was thus a model of ionic bonds. Both Lewis and Kossel structured their bonding models on that of Abegg’s rule (1904).

In 1927, the first mathematically complete quantum description of a simple chemical bond, i.e. that produced by one electron in the hydrogen molecular ion, H₂⁺, was derived by the Danish physicist Oyvind Burrau. This work showed that the quantum approach to chemical bonds could be fundamentally and quantitatively correct, but the mathematical methods used could not be extended to molecules containing more than one electron. A more practical, albeit less quantitative, approach was put forward in the same year by Walter Heitler and Fritz London. The Heitler-London method forms the basis of what is now called valence bond theory. In 1929, the linear combination of atomic orbitals molecular orbital method (LCAO) approximation was introduced by Sir John Lennard-Jones, who also suggested methods to derive electronic structures of molecules of F₂ (fluorine) and O₂ (oxygen) molecules, from basic quantum principles. This molecular orbital theory represented a covalent bond as an orbital formed by combining the quantum mechanical Schrödinger atomic orbitals which had been hypothesized for electrons in single atoms. The equations for bonding electrons in multi-electron atoms could not be solved to mathematical perfection (i.e., analytically), but approximations for them still gave many good qualitative predictions and results. Most quantitative calculations in modern quantum chemistry use either valence bond or molecular orbital theory as a starting point, although a third approach, Density Functional Theory, has become increasingly popular in recent years.

In 1935, H. H. James and A. S. Coolidge carried out a calculation on the dihydrogen molecule that, unlike all previous calculation which used functions only of the distance of the electron from the atomic nucleus, used functions which also explicitly added the distance between the two electrons. With up to 13 adjustable parameters they obtained a result very close to the experimental result for the dissociation energy. Later extensions have used up to 54 parameters and give excellent agreement with experiment. This calculation convinced the scientific community that quantum theory could give agreement with experiment. However this approach has none of the physical pictures of the valence bond and molecular orbital theories and is difficult to extend to larger molecules.

6. The mechanisms of formation of the covalent bond and it properties. The valence bond theory.

The foundations of modern chemical bonding theory were laid in 1916–1920 by G.N. Lewis and I. Langmuir who suggested that ionic species were formed by electron transfer, while electron sharing was important in covalent molecules. In some cases, it was suggested that the shared electrons in a bond were provided by one of the atoms but that once the bond (sometimes called a coordinate bond) is formed, it is indistinguishable from a ‘normal’ covalent bond.

Lewis presented a simple, but useful, method of describing the arrangement of valence electrons in molecules. The approach uses dots (or dots and crosses) to represent the number of valence electrons, and the nuclei are indicated by appropriate elemental symbols. A basic premise of the theory is that electrons in a molecule should be paired; the presence of a single (odd) electron indicates that the species is a radical.

A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms, and other covalent bonds. In short, the stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding.

Covalent bonding includes many kinds of interaction, including σ-bonding, π-bonding, metal to metal bonding, agostic interactions, and three-center two-electron bonds. The term covalent bond dates from 1939. The prefix co- means jointly, associated in action, partnered to a lesser degree, etc.; thus a “co-valent bond”, essentially, means that the atoms share “valence”, such as is discussed in valence bond theory. In the molecule H₂, the hydrogen atoms share the two electrons via covalent bonding. Covalency is greatest between atoms of similar electronegativities. Thus, covalent bonding does not necessarily require the two atoms be of the same elements, only that they be of comparable electronegativity. Although covalent bonding entails sharing of electrons, it is not necessarily delocalized. Furthermore, in contrast to electrostatic interactions (“ionic bonds”) the strength of covalent bond depends on the angular relation between atoms in polyatomic molecules.

Shared electrons must be belong to the both interaction atoms at the same time In this way each of the atoms that form the chemical bond reach the state of completed outer shell electronic level.

 

Polarity of covalent bonds.

Covalent bonds are affected by the electronegativity of the connected atoms. Two atoms with equal electronegativity will make non-polar covalent bonds such as H-H. An unequal relationship creates a polar covalent bond such as with H-Cl.

Subdivision of covalent bonds.

There are three types of covalent substances: individual molecules, molecular structures, and macromolecular structures. Individual molecules have strong bonds which hold the atoms together, but there are negligible forces of attraction between molecules. Such covalent substances are gases. For example, HCl, SO₂, CO₂, and CH₄. In molecular structures there are weak forces of attraction. Such covalent substances are low boiling temperature liquids (such as ethanol), and low melting temperature solids (such as iodine and solid CO₂). Macromolecular structures have large numbers of atoms linked in chains or sheets (such as graphite), or in 3-dimensional structures (such as diamond and quartz). These substances have a high melting and boiling points.

Some very simple covalent molecules of Chlorine.

For example, two chlorine atoms could both achieve stable structures by sharing their single unpaired electron as in the diagram.

 

The fact that one chlorine has been drawn with electrons marked as crosses and the other as dots is simply to show where all the electrons come from. In reality there is no difference between them.

The two chlorine atoms are said to be joined by a covalent bond. The reason that the two chlorine atoms stick together is that the shared pair of electrons is attracted to the nucleus of both chlorine atoms.

For example, Hydrogen atoms only need two electrons in their outer level to reach the noble gas structure of helium. Once again, the covalent bond holds the two atoms together because the pair of electrons is attracted to both nuclei. It’s fact that hydrogen molecule can be formed at the interaction of atoms which have the electrons with antiparallel spin.

Chemical bond is formed when the energy of the formation system will be less than the sum of energy of two isolated atoms.

1)     Electrostatic forces of attraction exist  between the positive nucleus of one inerection atom and the negative electrons of another atom (when the distance between interaction atoms is minimal)

2)      Decrease the energy of the system to minimal.

3)      Forms the the common electron-pair between interection atoms. The density of electrons increases between the nucleus of the interection atoms.

4)      The atomic orbital overlap each other during the formation of chemical bond.

5)      Hybridization of overlapping orbitals.

For example,

Hydrogen chloride. The hydrogen has a helium structure, and the chlorine an argon structure. Covalent bonding at A’level

Cases where there isn’t any difference from the simple view.

If you stick closely to modern A’level syllabuses, there is little need to move far from the simple (GCSE) view. The only thing which must be changed is the over-reliance on the concept of noble gas structures. Most of the simple molecules you draw do in fact have all their atoms with noble gas structures.

For example:

Even with a more complicated molecule like PCl₃, there’s no problem. In this case, only the outer electrons are shown for simplicity. Each atom in this structure has inner layers of electrons of 2,8. Again, everything present has a noble gas structure.

Cases where the simple view throws up problems

For example, Boron trifluoride, BF_3.

A boron atom only has 3 electrons in its outer level, and there is no possibility of it reaching a noble gas structure by simple sharing of electrons. Is this a problem? No. The boron has formed the maximum number of bonds that it can in the circumstances, and this is a perfectly valid structure.

Energy is released whenever a covalent bond is formed. Because energy is being lost from the system, it becomes more stable after every covalent bond is made. It follows, therefore, that an atom will tend to make as many covalent bonds as possible. In the case of boron in BF₃, three bonds is the maximum possible because boron only has 3 electrons to share.

Note:  You might perhaps wonder why boron doesn’t form ionic bonds with fluorine instead. Boron doesn’t form ions because the total energy needed to remove three electrons to form a B³⁺ ion is simply too great to be recoverable when attractions are set up between the boron and fluoride ions.

Phosphorus(V) chloride, PCl₅

In the case of phosphorus 5 covalent bonds are possible – as in PCl₅.

Phosphorus forms two chlorides – PCl₃ and PCl₅. When phosphorus burns in chlorine both are formed – the majority product depending on how much chlorine is available. We’ve already looked at the structure of PCl₃.

The diagram of PCl₅ (like the previous diagram of PCl₃) shows only the outer electrons.

Notice that the phosphorus now has 5 pairs of electrons in the outer level – certainly not a noble gas structure. You would have been content to draw PCl₃ at GCSE, but PCl₅ would have looked very worrying.

Why does phosphorus sometimes break away from a noble gas structure and form five bonds? In order to answer that question, we need to explore territory beyond the limits of current A’level syllabuses. Don’t be put off by this! It isn’t particularly difficult, and is extremely useful if you are going to understand the bonding in some important organic compounds.

What is wrong with the dots-and-crosses picture of bonding in methane?

We are starting with methane because it is the simplest case which illustrates the sort of processes involved. You will remember that the dots-and-crossed picture of methane looks like this.

There is a serious mis-match between this structure and the modern electronic structure of carbon, 1s²2s²2p_x¹2p_y¹. The modern structure shows that there are only 2 unpaired electrons for hydrogens to share with, instead of the 4 which the simple view requires.

You can see this more readily using the electrons-in-boxes notation. Only the 2-level electrons are shown. The 1s² electrons are too deep inside the atom to be involved in bonding. The only electrons directly available for sharing are the 2p electrons. Why then isn’t methane CH₂?

Promotion of an electron

When bonds are formed, energy is released and the system becomes more stable. If carbon forms 4 bonds rather than 2, twice as much energy is released and so the resulting molecule becomes even more stable.

There is only a small energy gap between the 2s and 2p orbitals, and so it pays the carbon to provide a small amount of energy to promote an electron from the 2s to the empty 2p to give 4 unpaired electrons. The extra energy released when the bonds form more than compensates for the initial input.

The carbon atom is now said to be in an excited state.

Note:  People sometimes worry that the promoted electron is drawn as an up-arrow, whereas it started as a down-arrow. The reason for this is actually fairly complicated – well beyond the level we are working at. Just get in the habit of writing it like this because it makes the diagrams look tidy!

Now that we’ve got 4 unpaired electrons ready for bonding, another problem arises. In methane all the carbon-hydrogen bonds are identical, but our electrons are in two different kinds of orbitals. You aren’t going to get four identical bonds unless you start from four identical orbitals.

A simple view of double covalent bonds

A double covalent bond is where two pairs of electrons are shared between the atoms rather than just one pair.

Some simple molecules containing double bonds

Oxygen, O₂

Two oxygen atoms can both achieve stable structures by sharing two pairs of electrons as in the diagram.

The double bond is shown conventionally by two lines joining the atoms. Each line represents one pair of shared electrons.

Carbon dioxide, CO₂

Ethene, C₂H₄

Ethene has a double bond between the two carbon atoms.

A more sophisticated view of the bonding in ethane.

It is important to explore the bonding in ethene in more detail because it has a direct impact on its chemistry. Unless you have some understanding of the true nature of the double bond, you can’t really understand the way that ethene behaves.

An orbital view of the bonding in ethene

Ethene is built from hydrogen atoms (1s¹) and carbon atoms (1s²2s²2p_x¹2p_y¹).

Promotion of an electron

The carbon atom doesn’t have enough unpaired electrons to form the required number of bonds, so it needs to promote one of the 2s² pair into the empty 2p_z orbital. This is exactly the same as happens whenever carbon forms bonds – whatever else it ends up joined to.

The carbon atom is now in an excited state.

 

Co-ordinate Covalent Bonds

a single covalent bond in which both electrons in a shared pair come from the same atom. The donor atom provides both electrons to a co-ordinate covalent bond, and the acceptor atom accepts an electron pair for sharing a co-ordinate covalent bond.

For example: a hydrogen ion unites with an ammonia molecule by a co-ordinate covalent bond to form the ammonium ion;

All four hydrogen atoms and all four N-H bonds in the ammonium ion are found by experiment to be equivalent.

Frequently nonmetal atoms that are already part of molecules or ions form co-ordinate covalent bonds with metal atoms or ions, usually those of transition metals. For example, the nitrogen atom in ammonia can “co-ordinate” with the silver cation to form what is called a complex ion;

Neutral compounds with similar co-ordinate covalent bonding can also be formed, notably by carbon monoxide and metal atoms;

 

Nonpolar and Polar Covalent Bonds

In molecules such as H₂, Cl₂, and N₂, the electron density (the probability of finding the valence electrons in a given area) is equally divided between the two bonded atoms. In a covalent bond of this type – a nonpolar covalent bond – the electrons are equally shared.

Whenever atoms of the two different elements are covalently bonded, the sharing of the electrons becomes unequal, because no two atoms of different elements have exactly the same electron-attracting ability. The electron density around one atom becomes greater than that around the other.

How unequally the electrons are shared depends on the relative abilities of the two different atoms to attract electrons.

A covalent bond in which electrons are shared unequally is called a polar covalent bond; one atom acquires a partial negative charge (d -) and the other acquires a partial positive charge (d +).

These are not unit charges, but only represent a reorientation, a sort of pushing around, of the total electron density of the two bonded atoms. The entire molecule remains electrically neutral.

A polar molecule is a dipole – a pair of opposite charges of equal magnitude at a specific distance from each other.

Example:

H₃C-CF₃

trifluoroethane

Valence bond (VB) theory is one of two basic theories, along with molecular orbital (MO) theory, that developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule. In 1927, valence bond theory was formulated and argued that a chemical bond forms when two valence electrons, in their respective atomic orbitals, work or function to hold two nuclei together, by virtue of system energy lowering effects. Building on this theory, chemist Linus Pauling published in 1931 what some consider one of the most important papers in the history of chemistry: “On the Nature of the Chemical Bond”. In this paper, elaborating on the works of Lewis, and the valence bond theory (VB) of Heitler and London, and his own earlier work, he presented six rules for the shared electron bond, the first three of which were already generally known:

1. The electron-pair bond forms through the interaction of an unpaired electron on each of two atoms.

2. The spins of the electrons have to be opposed.

3. Once paired, the two electrons cannot take part in additional bonds.

His last three rules were new:

4. The electron-exchange terms for the bond involves only one wave function from each atom.

5. The available electrons in the lowest energy level form the strongest bonds.

6. Of two orbitals in an atom, the one that can overlap the most with an orbital from another atom will form the strongest bond, and this bond will tend to lie in the direction of the concentrated orbital.

Building on this article, Pauling’s 1939 textbook: On the Nature of the Chemical Bond would become what some have called the “bible” of modern chemistry. This book helped experimental chemists to understand the impact of quantum theory on chemistry. However, the later edition in 1959 failed to address adequately the problems that appeared to be better understood by molecular orbital theory. The impact of valence theory declined during the 1960s and 1970s as molecular orbital theory grew in popularity and was implemented in many large computer programs. Since the 1980s, the more difficult problems of implementing valence bond theory into computer programs have been largely solved and valence bond theory has seen a resurgence.

 

7. The hybridization of atomic orbitals. Spatial structure of molecules. Polar and unpolar molecules. An ionic bond.

The word ‘hybridization’ means ‘mixing’ and when used in the context of atomic orbitals, it describes a way of deriving spatially directed orbitals which may be used within VB theory. Like all bonding theories, orbital hybridization is a model, and should not be taken to be a real phenomenon. Hybrid orbitals may be formed by mixing the characters of atomic orbitals that are close in energy. The character of a hybrid orbital depends on the atomic orbitals involved and their percentage contributions. The labels given to hybrid orbitals reflect the contributing atomic orbitals, e.g. an sp hybrid possesses equal amounts of s and p orbital character.

Hybrid orbitals are generated by mixing the characters of atomic orbitals.

sp Hybridization: a scheme for linear species.

The notation sp means that one s atomic orbital and one p atomic orbital mix to form a set of two hybrid orbitals with different directional properties.

Let us consider the combination of 2s, 2px and 2py atomic orbitals. The final hybrid orbitals must be equivalent in every way except for their directional properties; sp² hybrids must contain the same amount of s character as each other and the same amount of p character as one another. We begin by giving one-third of the 2s character to each sp² hybrid orbital.

For examples,

A non-existent compound – NCl₅

Nitrogen is in the same Group of the Periodic Table as phosphorus, and you might expect it to form a similar range of compounds. In fact, it doesn’t. For example, the compound NCl₃ exists, but there is no such thing as NCl₅.

Nitrogen is 1s²2s²2p_x¹2p_y¹2p_z¹. The reason that NCl₅ doesn’t exist is that in order to form five bonds, the nitrogen would have to promote one of its 2s electrons. The problem is that there aren’t any 2d orbitals to promote an electron into – and the energy gap to the next level (the 3s) is far too great.

In this case, then, the energy released when the extra bonds are made isn’t enough to compensate for the energy needed to promote an electron – and so that promotion doesn’t happen.

Atoms will form as many bonds as possible provided it is energetically profitable.

In the case of ethene, there is a difference from methane because each carbon is only joining to three other atoms rather than four. When the carbon atoms hybridise their outer orbitals before forming bonds, this time they only hybridise three of the orbitals rather than all four. They use the 2s electron and two of the 2p electrons, but leave the other 2p electron unchanged.

Note:  You might wonder why it chooses to hybridise these three orbitals rather than just use the three p orbitals which already have the same energy. It’s because it uses the orbitals with the lowest energy first.

The new orbitals formed are called sp² hybrids, because they are made by an s orbital and two p orbitals reorganising themselves. sp² orbitals look rather like sp³ orbitals that we discussed in the bonding in methane in the page on single bonds, except that they are shorter and fatter. The three sp² hybrid orbitals arrange themselves as far apart as possible – which is at 120° to each other in a plane. The remaining p orbital is at right angles to them.

The two carbon atoms and four hydrogen atoms would look like this before they joined together:

The various atomic orbitals which are pointing towards each other now merge to give molecular orbitals, each containing a bonding pair of electrons. Molecular orbitals made by end-to-end overlap of atomic orbitals are called sigma bonds.

The p orbitals on each carbon aren’t pointing towards each other, and so we’ll leave those for a moment. In the diagram, the black dots represent the nuclei of the atoms.

Notice that the p orbitals are so close that they are overlapping sideways.

This sideways overlap also creates a molecular orbital, but of a different kind. In this one the electrons aren’t held on the line between the two nuclei, but above and below the plane of the molecule. A bond formed in this way is called a pi bond.

For clarity, the sigma bonds are shown using lines – each line representing one pair of shared electrons. The various sorts of line show the directions the bonds point in. An ordinary line represents a bond in the plane of the screen (or the paper if you’ve printed it), a broken line is a bond going back away from you, and a wedge shows a bond coming out towards you.

Note:  The really interesting bond in ethene is the pi bond. In almost all cases where you will draw the structure of ethene, the sigma bonds will be shown as lines.

Be clear about what a pi bond is. It is a region of space in which you can find the two electrons which make up the bond. Those two electrons can live anywhere within that space. It would be quite misleading to think of one living in the top and the other in the bottom.

Taking chemistry further:  This is a good example of the curious behaviour of electrons. How do the electrons get from one half of the pi bond to the other if they are never found in between? It’s an unanswerable question if you think of electrons as particles. If you want to follow this up, you will have to read some fairly high-powered stuff on the wave nature of electrons.

Even if your syllabus doesn’t expect you to know how a pi bond is formed, it will expect you to know that it exists. The pi bond dominates the chemistry of ethene. It is very vulnerable to attack – a very negative region of space above and below the plane of the molecule. It is also somewhat distant from the control of the nuclei and so is a weaker bond than the sigma bond joining the two carbons.

All double bonds (whatever atoms they might be joining) will consist of a sigma bond and a pi bond.

This orbital view of the double bond is only really important at this level with regard to organic compounds. If you want to read more about this, follow the first link below which leads you to the menu for a section specifically on organic bonding. You will find the description of ethene repeated, but will also find information about the bonding in benzene and in the carbon-oxygen double bond.

This reorganises the electrons into four identical hybrid orbitals called sp³ hybrids (because they are made from one s orbital and three p orbitals). You should read “sp³” as “s p three” – not as “s p cubed”.

sp³ hybrid orbitals look a bit like half a p orbital, and they arrange themselves in space so that they are as far apart as possible. You can picture the nucleus as being at the centre of a tetrahedron (a triangularly based pyramid) with the orbitals pointing to the corners. For clarity, the nucleus is drawn far larger than it really is.

What happens when the bonds are formed?

Remember that hydrogen’s electron is in a 1s orbital – a spherically symmetric region of space surrounding the nucleus where there is some fixed chance (say 95%) of finding the electron. When a covalent bond is formed, the atomic orbitals (the orbitals in the individual atoms) merge to produce a new molecular orbital which contains the electron pair which creates the bond.

Four molecular orbitals are formed, looking rather like the original sp³ hybrids, but with a hydrogeucleus embedded in each lobe. Each orbital holds the 2 electrons that we’ve previously drawn as a dot and a cross.

The principles involved – promotion of electrons if necessary, then hybridisation, followed by the formation of molecular orbitals – can be applied to any covalently-bound molecule.

Note:  You will find this bit on methane repeated in the organic section of this site. That article on methane goes on to look at the formation of carbon-carbon single bonds in ethane.

The bonding in the phosphorus chlorides, PCl₃ and PCl₅

What’s wrong with the simple view of PCl₃?

This diagram only shows the outer (bonding) electrons.

Nothing is wrong with this! (Although it doesn’t account for the shape of the molecule properly.) If you were going to take a more modern look at it, the argument would go like this:

Phosphorus has the electronic structure 1s²2s²2p⁶3s²3p_x¹3p_y¹3p_z¹. If we look only at the outer electrons as “electrons-in-boxes”:

There are 3 unpaired electrons that can be used to form bonds with 3 chlorine atoms. The four 3-level orbitals hybridise to produce 4 equivalent sp³ hybrids just like in carbon – except that one of these hybrid orbitals contains a lone pair of electrons.

Each of the 3 chlorines then forms a covalent bond by merging the atomic orbital containing its unpaired electron with one of the phosphorus unpaired electrons to make 3 molecular orbitals.

You might wonder whether all this is worth the bother! Probably not! It is worth it with PCl₅, though.

What’s wrong with the simple view of PCl₅?

You will remember that the dots-and-crosses picture of PCl₅ looks awkward because the phosphorus doesn’t end up with a noble gas structure. This diagram also shows only the outer electrons.

In this case, a more modern view makes things look better by abandoning any pretence of worrying about noble gas structures.

If the phosphorus is going to form PCl₅ it has first to generate 5 unpaired electrons. It does this by promoting one of the electrons in the 3s orbital to the next available higher energy orbital.

Which higher energy orbital? It uses one of the 3d orbitals. You might have expected it to use the 4s orbital because this is the orbital that fills before the 3d when atoms are being built from scratch. Not so! Apart from when you are building the atoms in the first place, the 3d always counts as the lower energy orbital.

This leaves the phosphorus with this arrangement of its electrons:

The 3-level electrons now rearrange (hybridise) themselves to give 5 hybrid orbitals, all of equal energy. They would be called sp³d hybrids because that’s what they are made from.

The electrons in each of these orbitals would then share space with electrons from five chlorines to make five new molecular orbitals – and hence five covalent bonds.

Why does phosphorus form these extra two bonds? It puts in an amount of energy to promote an electron, which is more than paid back when the new bonds form. Put simply, it is energetically profitable for the phosphorus to form the extra bonds.

The advantage of thinking of it in this way is that it completely ignores the question of whether you’ve got a noble gas structure, and so you don’t worry about it.

Molecular Geometry (three dimensional structure) can be determined by the number of s-bonds and the lone pairs on the central atom. These lone pairs will also be accommodated in hybridized orbitals.

Orbitals used in bond formation	s-bond, showing the head on overlap of atomic orbitals
s-orbital – s-orbital
s-orbital – p-orbital
p-orbital – p-orbital
sp-hybrid orbital – sp-hybrid orbital or sp-hybrid – sp2 hybrid or sp2 hybrid – sp2 hybrid or sp2 hybrid – sp3 hybrid or sp2 hybrid – sp3d hybrid or sp3 hybrid – sp3d2 hybrid and so on	Two overlapping hybrids, forming a strong bond. Hybridized orbitals will be simplified like so

 

Hybridization and associated Molecular Geometry

Hybridization, Lone Pairs and associated Molecular Geometry.

Molecular Geometry is determined by the positions of atomic nuclei in three dimensional space

 

Polar and Non-Polar Molecules

The arrangement or geometry of the atoms in some molecules is such that one end of the molecule has a positive electrical charge and the other side has a negative charge. If this is the case, the molecule is called a polar molecule, meaning that it has electrical poles. Otherwise, it is called a non-polar molecule. Whether molecules are polar or non-polar determines if they will mix to form a solution or that they don’t mix well together.

Polar molecules

Chemical bonding is the result of either an atom sharing one or more outer orbit electrons with another atom or an atom taking outer orbit electrons from the atom with which it is bonding. Normally, an atom has an even distribution of electrons in the orbits or shells, but if more end up on one side that the other in a molecule, there can be a resulting electrical field in that area.

For example, Water. Water is a polar molecule because of the way the atoms bind in the molecule such that there are excess electrons on the Oxygen side and a lack or excess of positive charges on the Hydrogen side of the molecule.

Water is a polar molecule with positive charges on one side and negative on the other

For example, Water

Examples of polar molecules of materials that are gases under standard conditions are: Ammonia (NH₃), Sulfur Dioxide (SO₂) and Hydrogen Sulfide (H₂S).

Non-polar molecules

A non-polar molecule is one that the electrons are distributed more symmetrically and thus does not have an abundance of charges at the opposite sides. The charges all cancel out each other.

The electrical charges ion-polar Carbon Dioxide are evenly distributed

For example, Liquids

Most hydrocarbons are non-polar molecules. Examples include Toluene and Gasoline. (See Hydrocarbon Bonding for more information.)

For example, Gases

Common examples of non-polar gases are the noble or inert gases, including Helium (He), Neon (Ne), Krypton (Kr) and Xenon (Xe). Other non-polar gases include the Hydrogen (H₂), Nitrogen (N₂), Oxygen (O₂), Carbon Dioxide (CO₂), Methane (CH₄) and Ethylene (C₂H₄) molecules.

Rule for solutions

The rule for determining if a mixture becomes a solution is that polar molecules will mix to form solutions and non-polar molecules will form solutions, but a polar and non-polar combination will not form a solution.

Water is a polar molecule and oil is a non-polar molecule. Thus they won’t form a solution. On the other hand, since alcohol is a polar molecule, it will form a solution with water.

An ionic bond is a type of chemical bond that involves a metal and a nonmetal ion (or polyatomic ions such as ammonium) through electrostatic attraction. In short, it is a bond formed by the attraction between two oppositely charged ions. The metal donates one or more electrons, forming a positively charged ion or cation with a stable electron configuration. These electrons then enter the non metal, causing it to form a negatively charged ion or anion which also has a stable electron configuration. The electrostatic attraction between the oppositely charged ions causes them to come together and form a bond. For example, common table salt is sodium chloride. When sodium (Na) and chlorine (Cl) are combined, the sodium atoms each lose an electron, forming cations (Na⁺), and the chlorine atoms each gain an electron to form anions (Cl¯). These ions are then attracted to each other in a 1:1 ratio to form sodium chloride (NaCl). Na + Cl → Na⁺ + Cl ¯ → NaCl

Electron configurations of lithium and fluorine. Lithium has one electron in its outer shell, held rather loosely because the ionization energy is low. Fluorine carries 7 electrons in its outer shell. When one electron moves from lithium to fluorine, each ion acquires the noble gas configuration. The bonding energy from the electrostatic attraction of the two oppositely charged ions has a large enough negative value that the overall bonded state energy is lower than the unbonded state. The removal of electrons from the atoms is endothermic and causes the ions to have a higher energy. There may also be energy changes associated with breaking of existing bonds or the addition of more than one electron to form anions. However, the attraction of the ions to each other lowers their energy.

Ionic bonding will occur only if the overall energy change for the reaction is favourable – when the bonded atoms have a lower energy than the free ones. The larger the resulting energy change the stronger the bond. The low electronegativity of metals and high electronegativity of non-metals means that the energy change of the reaction is most favorable when metals lose electrons and non-metals gain electrons.

Pure ionic bonding is not known to exist. All ionic compounds have a degree of covalent bonding. The larger the difference in electronegativity between two atoms, the more ionic the bond. Ionic compounds conduct electricity when molten or in solution. They generally have a high melting point and tend to be soluble in water.

8. The method of molecular orbitals (MO). The types of МО and their properties. Multipleness of bond in ММО. Intermolecular interaction. A hydrogen bond.

In molecular orbital (MO) theory, we begin by placing the nuclei of a given molecule in their equilibrium positions and then calculate the molecular orbitals (i.e. regions of space spread over the entire molecule) that a single electron might occupy. Each MO arises from interactions between orbitals of atomic centres in the molecule, and such interactions are:

1. allowed if the symmetries of the atomic orbitals arecompatible with one another;

2. efficient if the region of overlap between the two atomic orbitals is significant;

3.efficient if the atomic orbitals are relatively close in energy

An important ground-rule of MO theory is that the number of MOs that can be formed must equal the number of atomic orbitals of the constituent atoms.

The goal of molecular orbital theory is to describe molecules in a similar way to how we describe atoms, that is, in terms of orbitals, orbital diagrams, and electron configurations. For example, to give you a glimpse at where we are headed, the following are orbital diagrams for O₂ and O.

                   O₂                                                          O

Each line in the molecular orbital diagram represents a molecular orbital, which is the volume within which a high percentage of the negative charge generated by the electron is found. The molecular orbital volume encompasses the whole molecule. We assume that the electrons would fill the molecular orbitals of molecules like electrons fill atomic orbitals in atoms.

·         The molecular orbitals are filled in a way that yields the lowest potential energy for the molecule.

·         The maximum number of electrons in each molecular orbital is two. (We follow the Pauli exclusion principle.)

·         Orbitals of equal energy are half filled with parallel spin before they begin to pair up. (We follow Hund’s Rule.)

Before we continue with a description of a model used to generate molecular orbital diagrams, lets get a review of light and electron waves and how two waves can interact. The wave description of light describes the effect that the light has on the space around it. This effect is to generate an oscillating electric and magnetic fields. These fields can vary in intensity, which is reflected in varying brightness of light. 

The wave description of the electron describes the variation in the intensity of negative charge generated by the electron.

Light waves can interact in-phase, which leads to an increase in the intensity of the light (brighter) and out-of-phase, which leads to a decrease in the intensity of the light (less bright). Electron waves can also interact in-phase and out-of-phase. In-phase interaction leads to an increase in the intensity of the negative charge. Out-of-phase interaction leads to a decrease in the intensity of the negative charge.

One common approximation that allows us to generate molecular orbital diagrams for some small diatomic molecules is called the Linear Combination of Atomic Orbitals (LCAO) approach. The following assumptions lie at the core of this model.

·         Molecular orbitals are formed from the overlap of atomic orbitals.

·         Only atomic orbitals of about the same energy interact to a significant degree.

·         When two atomic orbitals overlap, they interact in two extreme ways to form two molecular orbitals, a bonding molecular orbital and an antibonding molecular orbital.

For example, our model assumes that two 1s atomic orbitals can overlap in two extreme ways to form two molecular orbitals. One of the ways the atomic orbitals interact is in-phase, which leads to wave enhancement similar to the enhancement of two in-phase light waves. Where the atomic orbitals overlap, the in-phase interaction leads to an increase in the intensity of the negative charge in the region where they overlap. This creates an increase iegative charge between the nuclei and an increase in the plus-minus attraction between the electron charge and the nuclei for the atoms in the bond. The greater attraction leads to lower potential energy. Because electrons in the molecular orbital are lower potential energy than in separate atomic orbitals, energy would be required to shift the electrons back into the 1s orbitals of separate atoms. This keeps the atoms together in the molecule, so we call this orbital a bonding molecular orbital. The molecular orbital formed is symmetrical about the axis of the bond. Symmetrical molecular orbitals are called sigma, σ, molecular orbitals. The symbol σ_1s is used to describe the bonding molecular orbital formed from two 1s atomic orbitals.

The second way that two atomic orbitals interact is out-of-phase. Where the atomic orbitals overlap, the out-of-phase interaction leads to a decrease in the intensity of the negative charge. This creates a decrease iegative charge between the nuclei and a decrease in the plus-minus attraction between the electron charge and the nuclei for the atoms in the bond. The lesser attraction leads to higher potential energy. The electrons are more stable in the 1s atomic orbitals of separate atoms, so electrons in this type of molecular orbital destabilize the bond between atoms. We call molecular orbitals of this type antibonding molecular orbitals. The molecular orbital formed is symmetrical about the axis of the bond, so it is a sigma molecular orbital with a symbol of σ*_1s. The asterisk indicates an antibonding molecular orbital. 

When two larger atoms atoms combine to form a diatomic molecule (like O₂, F₂, or Ne₂), more atomic orbitals interact. The LCAO approximation assumes that only the atomic orbitals of about the same energy interact. For O₂, F₂, or Ne₂, the orbital energies are different enough so only orbitals of the same energy interact to a significant degree. 

Like for hydrogen, the 1s from one atom overlaps the 1s from the other atom to form a σ_1s bonding molecular orbital and a σ*_1s antibonding molecular orbital. The shapes would be similar to those formed from the 1s orbitals for hydrogen. The 2s atomic orbital from one atom overlaps the 2s from the other atom to form a σ_2s bonding molecular orbital and a σ*_2s antibonding molecular orbital. The shapes of these molecular orbitals would be similar to those for the σ_1s and σ*_1s molecular orbitals. Both σ_2s and σ*_2s molecular orbitals are higher energy and larger than the σ_1s and σ*_1s molecular orbitals.

The p atomic orbitals of the two atoms can interact in two different ways, parallel or end-on. The molecular orbitals are different for each type of interaction. The end-on interaction between two 2p_x atomic orbitals yields sigma molecular orbitals, which are symmetrical about the axis of the bond.

The two 2p_y atomic orbitals overlap in parallel and form two pi molecular orbitals. Pi molecular orbitals are asymmetrical about the axis of the bond.

The 2p_z-2p_z overlap generates another pair of π_2p and π*_2p molecular orbitals. The 2p_z-2p_z overlap is similar to the The 2p_y-2p_y overlap. To visualize this overlap, picture all of the orbitals in the image above rotated 90 degrees so the axes that run through the atomic and molecular orbitals are perpendicular to the screen (paper). The molecular orbitals formed have the same potential energies as the molecular orbitals formed from the 2p_y-2p_y overlap. 

There is less overlap for the parallel atomic orbitals. When the interaction is in-phase, less overlap leads to less electron charge enhancement between the nuclei. This leads to less electron charge between the nuclei for the pi bonding molecular orbital than for the sigma bonding molecular orbital. Less electron character between the nuclei means less plus-minus attraction, less stabilization, and higher potential energy for the pi bonding molecular orbital compared to the sigma bonding molecular orbital.

When the interaction is out-of-phase, less overlap leads to less shift of electron charge from between the nuclei. This leads to more electron charge between the nuclei for the pi antibonding molecular orbital than for the sigma antibonding molecular orbital. More electron charge between the nuclei means more plus-minus attraction and lower potential energy for the pi antibonding molecular orbital compared to the sigma antibonding molecular orbital. 

The expected molecular orbital diagram from the overlap of 1s, 2s and 2p atomic orbitals is as follows. We will use this diagram to describe O₂, F₂, Ne₂, CO, and NO.

We use the following procedure when drawing molecular orbital diagrams.

· Determine the number of electrons in the molecule. We get the number of electrons per atom from their atomic number on the periodic table. (Remember to determine the total number of electrons, not just the valence electrons.)

· Fill the molecular orbitals from bottom to top until all the electrons are added. Describe the electrons with arrows. Put two arrows in each molecular orbital, with the first arrow pointing up and the second pointing down.

· Orbitals of equal energy are half filled with parallel spin before they begin to pair up.

We describe the stability of the molecule with bond order.

  bond order  =  1/2 (#e- in bonding MO’s – #e- in antibonding MO’s)

We use bond orders to predict the stability of molecules.

· If the bond order for a molecule is equal to zero, the molecule is unstable.

· A bond order of greater than zero suggests a stable molecule.

· The higher the bond order is, the more stable the bond.

We can use the molecular orbital diagram to predict whether the molecule is paramagnetic or diamagnetic. If all the electrons are paired, the molecule is diamagnetic. If one or more electrons are unpaired, the molecule is paramagnetic.

EXAMPLES: 

1. The molecular orbital diagram for a diatomic hydrogen molecule, H₂, is:

·The bond order is 1.      Bond Order  =  1/2(2 – 0)  =  1

· The bond order above zero suggests that H₂ is stable.

· Because there are no unpaired electrons, H₂ is diamagnetic.

2. The molecular orbital diagram for a diatomic helium molecule, He₂, shows the following.

·The bond order is 0 for He₂.     Bond Order  =  1/2(2 – 2)  =  0

· The zero bond order for He₂ suggests that He₂ is unstable.

· If He₂ did form, it would be diamagnetic.

3. The molecular orbital diagram for a diatomic oxygen molecule, O₂, is

 

·O₂ has a bond order of 2.      Bond Order  =  1/2(10 – 6)  =  2

·  The bond order of two suggests that the oxygen molecule is stable.

· The two unpaired electrons show that O₂ is paramagnetic.

4. The molecular orbital diagram for a diatomic fluorine molecule, F₂, is

 

· F₂ has a bond order of 1.      Bond Order  =  1/2(10 – 8)  =  1

· The bond order of one suggests that the fluorine molecule is stable.

· Because all of the electrons are paired, F₂ is diamagnetic.

5. The molecular orbital diagram for a diatomic neon molecule, Ne₂, is

 

· Ne₂ has a bond order of 0.      Bond Order  =  1/2(10 – 10)  =  0

· The zero bond order for Ne₂ suggests that Ne₂ is unstable.

· If Ne₂ did form, it would be diamagnetic.

We can describe diatomic molecules composed of atoms of different elements in a similar way. The bond between the carbon and oxygen in carbon monoxide is very strong despite what looks like a strange and perhaps unstable Lewis Structure.

The plus formal charge on the more electronegative oxygen and the minus formal charge on the less electronegative carbon would suggest instability. The molecular orbital diagram predicts CO to be very stable with a bond order of three.

We predict the nitrogen monoxide molecule to be unstable according to the Lewis approach to bonding.

The unpaired electron and the lack of an octet of electrons around nitrogen would suggest an unstable molecule. NO is actually quite stable. The molecular orbital diagram predicts this by showing the molecule to have a bond order of 2.5.

A hydrogen bond is the attractive interaction of a hydrogen atom with an electronegative atom, such as nitrogen, oxygen or fluorine (thus the name “hydrogen bond,” which should not be confused with a covalent bond to hydrogen). The hydrogen must be covalently bonded to another electronegative atom to create the bond. These bonds can occur between molecules (intermolecularly), or within different parts of a single molecule (intramolecularly). The hydrogen bond (5 to 30 kJ/mole) is stronger than a van der Waals interaction, but weaker than covalent or ionic bonds. This type of bond occurs in both inorganic molecules such as water and organic molecules such as DNA.

Intermolecular hydrogen bonding is responsible for the high boiling point of water (100 °C) compared to the other group 16 hydrides that have no hydrogen bonds. Intramolecular hydrogen bonding is partly responsible for the secondary, tertiary, and quaternary structures of proteins and nucleic acids. It also plays an important role in the structure of polymers, both synthetic and natural.

Metallic bonding is the electromagnetic interaction between delocalized electrons, called conduction electrons and gathered in an “electron sea”, and the metallic nuclei within metals. Understood as the sharing of “free” electrons among a lattice of positively charged ions (cations), metallic bonding is sometimes compared with that of molten salts; however, this simplistic view holds true for very few metals. In a more quantum-mechanical view, the conduction electrons divide their density equally over all atoms that function as neutral (non-charged) entities. Metallic bonding accounts for many physical properties of metals, such as strength, malleability, ductility, thermal and electrical conductivity, opacity, and luster.

 

References:

1. The abstract of the lecture.

2. intranet.tdmu.edu.ua/auth.php

3. Atkins P. W. Physical chemistry / P.W. Atkins. – New York, 1994. – P.299‑307.

4. Cotton F. A. Chemical Applications of Group Theory / F. A. Cotton. ‑ John Wiley & Sons : New York, 1990.

5. Girolami G. S. Synthesis and Technique in Inorganic Chemistry / G. S. Girolami, T. B. Rauchfuss, R. J. Angelici. ‑ University Science Books : Mill Valley, CA, 1999.

6. Russell J. B. General chemistry / J B. Russell. New York.1992. – P. 550‑599.

7. Lawrence D. D. Analytical chemistry / D. D. Lawrence. –New York, 1992. – P. 218–224.

8. http://www.lsbu.ac.uk/water/ionish.html

 

Prepared by PhD Falfushynska H.