Question

(i) State Bohr's quantization condition for defining stationary orbits. How does the de Broglie hypothesis explain the stationary orbits?

(ii) Find the relation between three wavelengths λ₁, λ₂ and λ₃ from the energy-level diagram shown below.

Answer 1

(a) Bohr's quantisation condition: According to Bohr, an electron can revolve only in certain discrete, non-radiating orbits for which total angular momentum of the revolving electron is an integral multiple of `h/(2pi)`where h is the Planck's constant.

`:.mvr=(nh)/(2pi)`

(b) Using the Rydberg formula of the spectra of hydrogen atom, we write

`1/lamda_1=R(1/n_(2^2)-1/n_(3^2)) ......(1)`

`1/lamda_2=R(1/n_(1^2)-1/n_(2^2)) ......(2)`

`1/lamda_3=R(1/n_(1^2)-1/n_(3^2)) ......(3)`

Adding (1) and (2), we find that 

`1/lambda_1+1/(lambda_2)=R(1/n_(1^2)-1/n_(3^2))=1/lambda_3`

This is the required relation between the three wavelengths.