5. TOWARDS QUANTUM MECHANICAL MODEL OF THE ATOM

​​​​ TOWARDS QUANTUM MECHANICAL MODEL OF THE ATOM

• Dual Behaviour of Matter (de Broglie Equation)
de Broglie in 1924, proposed that matter, like radiation, should also exhibit dual behaviour i.e., both particle like and wave like properties. This means that like photons, electrons also have momentum as well as wavelength.
From this analogy, de Broglie gave the following relation between wavelength (λ) and momentum (p) of a material particle.

λ = h/mv
   = h/p
Where, m = mass of the particle
             v = velocity of particle
             p = momentum of the particle
this relationship has been verified by an experiment.

• Heisenberg’s Uncertainty Principle
It states that, “It is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron”. 

Mathematically it can be given as,
Δx × ΔP_x ≥ h/4π
Or
Δx × Δ(mv_x) ≥ h/4π
Or
Δx × Δv_x ≥  h/4πm
Where Δx is the uncertainty in position and ΔP_x (or ΔV_x) is the uncertainty in momentum (velocity) of the particle and h is ‘Plank’s constant.

• Significance of Uncertainty Principle
(i) It rules out existence of definite paths or trajectories of electrons and other similar particles.
(ii) The effect of Heisenberg’s uncertainty principle is significant only for microscopic objects and is negligible for macroscopic objects.

• Reasons for the Failure of Bohr Model
(i) The wave character of the electron is not considered in Bohr Model.
(ii) According to Bohr Model an orbit is a clearly defined path and this path can completely be defined only if both the position and the velocity of the electron are known exactly at the same time. This is not possible according to the Heisenberg’s uncertainty principle.