Atomic Structure

Dual Nature of Matter:

Wave and Particle nature

Experimental verification of the dual nature of electrons (matter):

Wave Nature

a) Davidson and Germer’s experiment showed that electron beams reflected or scattered from a crystal gave a diffraction pattern ( consisting of a number of concentric rings) This phenomenon can be explained only using the wave nature of electrons.

b) Thompson replaced the crystal by a gold foil and performed the above experiment and obtained a diffraction pattern which again confirmed the wave nature of electrons.

Particle nature

a) Scintillation effect: When electrons strike a Zinc Sulphide screen a spot of light know as Scintillation is produced. This is a localised effect characteristic of particles or matter.

b) Mass of electron and the determination of e/m ratio by Thompson determines the particle nature of radiation.

c) The rotation of the mica wheel by the electron beams in a cathode ray tube is characteristic of particle nature i.e. momentum of the electron is transferred to the paddle wheels.

Theoretical confirmation of the dual nature of matter:

De Broglie Relation:

In the case of a photon if it is assumed to have a wave character its energy is given by

E = hn (1) According to Planck’s theory where h is Planck’s constant and n is the frequency of a radiation.

If the photon is supposed to have a particle character, its energy is is given by

E = mc² (2) According to Einstein’s equation

From equations (1) and (2) mc² = hn , n = c/l , mc² = h c/l or l = h/mc for matter mc = mv where v is the velocity of matter or l = h/p p = momentum of an electron.

Quantum Numbers:

These are a set of 4 integers necessary to specify the energy , position, shape , size and orientation of orbitals to which electrons belong.

Principal Quantum Number ‘n’ :

It specifies the location and energy of an electron, It is a measure of the effective volume or size of the electron cloud denoted by ‘n’ and can have values 1,2,3,4..........¥

Azimuthal Quantum Number ‘l’ :

It determines the shape of the orbital. It takes integral values from 0 ® (n-1) where ‘n’ is the principal quantum number. When ‘l’ = 0, 1, 2, the shapes of the orbitals are ‘s’ Spherically symmetrical, ‘p’ dumbbell, and ‘d’ double dumbbell.

l	0	1	2	3	4
orbital	s	p	d	f	g
Shape	Spherically symmetrical	Dumbell	Double dumbell

Magnetic Moment Quantum Number ‘m’ : (2l+1) values

It gives the orientation of the orbitals in space. It takes integral values ranging from -l ......0 .....+l or ‘s’ orbital has got one orientation, ‘p’ orbital has got 3 orientations, ‘d’ orbital has got ‘5’ orientations and ‘f’ orbital has got 7 orientations.

Spin Quantum Number ‘s’ :

It indicates the direction in which the electron spins on its own axis or the magnetic property that is associated with it . This value is quantised the two vlues that are permitted are + ½ and - ½ where g = gyromagnetic constant.

Heisenbergs Uncertainty Principle:

It is impossible to measure simultaneously the position and momentum of a small particle (subatomic particle) with absolute accuracy or certainty

What is the significance of the uncertainty principle ?

Why the electron cannot exist in the nucleus?

Orbit	Orbital
It is a well defined circular path around the nucleus in which the electron revolves	It is a region in three dimensional space around the nucleus where there is a very high probability of locating the electron
It is circular in shape	‘s’, ‘p’ and ‘d’ orbitals are spherical, dumbbell and double dumbbell in shape respectively
It represents the movement of an electron around the nucleus in one plane.	It represents the movement of an electron around the nucleus in a three dimensional space.
It states with certainty the momentum and position of an electron. Violates the Heisenbergs uncertainty principle	It is a consequence of Heisenbergs uncertainty principle. .i.e. The position and momentum cannot be known with certainty
The maximum number of electrons in an orbit is 2n² .	The maximum no of electrons in an orbital is 2

The number of orbitals = n²

Degenerate Orbitals:

The orbitals of the same subshells having equal energy are called degenerate orbitals.

e.g. P_x, P_y and P_z orbitals. The 5 ‘d’ orbitals are degenerate but can loose their degeneracy under the influence of and external electrical or magnetic field.

Nodal Plane:

The plane passing through the nucleus on which the probability of finding the electron is almost zero is called Nodal plane

Schrodinger Wave Equation:

‘E’ is the total energy of the electron in the system and ‘V’ is the potential energy of the system.

It is known as an orbital wave function, which is a solution to the Schrodinger wave equation. It represents the amplitude of the wave and the significant values are Eigen functions.( The wave function Y by itself has no significance)

Y²

It represents the electron density or the probability of locating electrons of specific energy at different regions in space. It leads to the concept of orbitals.

Energy of an electron in the ground state of hydrogen atom:

E = -2.17 x 10^-18 J/Atom and -1.312x10⁶ J/Mole.

Why is the value of the energy of an electron negative?

The value of the energy of an electron in the hydrogen atom is negative because when the electron is far away from the nucleus the Potential Energy is taken as zero. When the electron comes closer to the nucleus work is done by the electron therefore energy is released and the energy of the electron becomes less than zero hence it has a negative value.

The difference in Energy between two energy levels viz. E₂ and E₁ when E₂ > E₁:

E₂ - E₁ = DE

The study of quantum numbers may be briefly summarised as follows:

Type Of Information

Principal Quantum Number

‘n’

Azimuthal Quantum Number ‘l’

Magnetic Moment Quantum Number ‘m’

Spin Quantum Number

‘s’

Why is it required

To explain the main lines of spectra

To explain the fine structure of line spectra

To explain the splitting of lines in the magnetic field

To explain the magnetic properties of substances.

Electronic Configuration of Elements:

Aufbau Principle:

According to the principle the electrons are filled in the various subshells in the order of their increasing energies.

(n + l) Rule: The subshell with lower n+l value will posses lower energy and will be filled first.

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 4f ......

Pauli’s Exclusion Principle:

No two electrons in an atom can have all the 4 quantum numbers alike.

Hund’s Rule of Maximum Multiplicity:

Electron pairing will not take place in degenerate orbitals (same energy subshell) until each orbital is first singly filled with electrons having parallel spins.

Why is it that the 4s electrons are lost during the formation of divalent ions in the first transition series e.g. Fe²⁺ & Ni²⁺?

· The 4s orbital is physically larger than 3d orbital hence present as the outer most electron (valence)

· The shielding effect of the inner electrons prevents the effective attraction of the 4s electrons by the nucleus. Therefore can be easily removed.

Exceptional Electronic Configuration:

Cu, Cr, Mo, Ag, W & Au have got exceptional electronic configuration. Explain.

Z = 29, 24, 42, 47, 74 & 79 Respectively.

Half Filled ‘d’ orbital configurations are preferred because

· There is extra stability because of the symmetrical distribution of the electrons in the orbitals.

· The Exchange energy is High for Cr, Mo & W.

· Exchange energy can be calculated using the following equation Where ‘n’ is the number of electrons having parallel spins. In the equation given below ‘n’ stands for the number of unpaired electrons in the d orbital.

Molecular Orbital Theory

This theory has been proposed by Hund and Mullicken

Basic Concept:

Atomic orbitals of atoms involved in the formation of a molecule get redistributed to give rise to an equivalent number of new molecular orbitals. During the process the identity of the atoms are lost. Linear combination of atomic orbitals leads to the formation of the molecular orbitals.

Bonding Molecular Orbitals y_mo:

A Constructive Interference leading to Addition Combination of wave fronts.

· A bonding molecular orbital is obtained by the addition combination of 2 atomic orbitals with same symmetry.

· There is an increased electron density between the two orbitals leading to decreased energy and increased stability

· Electrons in this orbital leads to attraction between the atoms.

· The energy of the bonding M.O is less than that of the Atomic orbitals.

Antibonding Molecular Orbital y^*_mo:

A Destructive Interference leading to Subtractive Combination of Wave fronts:

· An Antibonding molecular orbital is obtained by the Subtractive combination of 2 atomic orbitals with opposite symmetry.

· There is a decreased electron density between the two orbitals leading to decrease in stability

· Electrons in this orbital leads to repulsion between the atoms.

· The energy of the antibonding molecular orbital is greater than that of the atomic orbitals

Bond Order

It is a measure of the stability of the molecule

It can be calculated by the following relation where N_b stands for the electrons in the bonding molecular orbital and N_a stands for the number of electrons in the antibonding molecular orbital. B.O = ½[N_b - N_a] We can draw the following conclusions from the values of the bond order:

· A Positive value for the bond order indicates the stability or formation of the molecule.

· When the bond order is zero the molecule does not form or exist.

· A whole number value for the bond order can also indicate the number of covalent bonds in the molecule

· Bond order is directly proportional to Bond Dissociation Energy

· Bond order is inversely proportional to Bond Length

· When two molecules have the same bond order the molecule with more bonding electrons is more stable.

Examples of molecules showing exceptions in its electronic configuration are B₂,C₂&N₂.

Paramagnetic Behaviour of oxygen can only be explained using M.O. Theory. A molecule with unpaired electrons in a molecular orbital would show paramagnetic behaviour.

The aufbau order for regular diatomic molecules is illustrated below

For molecules like B₂., C₂, N₂ the following order may be used

This is an exception due to the repulsion between the s2p_zand the is p 2p orbitals, this configuration facilitates the electrons to have more unpaired electrons in accordance with Hund’s rule there by reducing the total repulsive energy generated by the expected regular configuration. This is in agreement with the magnetic behaviour exhibited by the molecules. Or rather this is the explanation for the magnetic behaviour exhibited by the respective molecules cited above.

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