Atomic structure and chemical bonding
This module deals with the study of the structure of atoms, leading to the electronic configurations of atoms, hybridisation of orbitals, molecular orbital method of bonding, shapes of molecules.
Dual Nature of Matter and Radiation and the de Broglie Relation
To explain the behaviour of visible light, Sir Issac Newton suggested the “Corpuscular” theory’ and Christian Huygens suggested the “wave” theory. Max Planck put forward the “photonic” theory of radiation. Einstein in 1905 suggested that any radiation has dual behaviour - as wave and particle.
In 1923, de Broglie suggested the matter-wave dualism: all matter, including electrons, have the dual character as particle and wave. He derived a relation, De Broglie equation, for the wave length of a particle
De Broglie equation
E = mc2, Einstein’s mass - energy relation, (as particle)
where E = energy, m = mass and c = velocity of light
E = hv, Planck’s relation, (energy of a photon), (as wave)
where E = energy, v = frequency of radiation and h is Planck’s constant
Equating them,
hu = mc2
But frequency v = where c is the velocity of light and l, is the wave length
Thus h = mc2 \= h/mc
l = h/mu where u velocity of the particle .
l = h/mu = h/p when P is the momentum.
de Broglie wavelength is appreciable for microscopic particles like the electrons and negligible for macroscopic particles.
The Bohr postulate, the angular momentum of an electron in an orbit (circular) is an integral multiple of h/2p , is justified by the de Broglie equation.
For a wave to be in phase - sustain permanently in the circle - the circumference of the circle must be an integral multiple of the wavelength.
ie. 2pr = nl, where r = radius and l, = wavelength.
But l, = h/mu (de Broglie relation)
Thus 2pr = n/mu
mur = n h/2p
(mur = angular momentum)
Heisenberg’s Uncertainty Principle
For any pair of interdependent or Conjugate properties - like the wave and particle nature of the electron- when one of the properties is precise, the other is uncertain. Due to the dual nature of the electron, it is very difficult to locate the exact position and know the exact velocity simultaneously. This is stated in
Heisenberg’s Uncertainty Principle
It is impossible to determine with precision, the exact position and
velocity (or momentum) of a small moving particle like the electron