Question

State Bohr’* postulates, obtain the expression for the total energy of the electron in the stationary states of the hydrogen atom. Hence draw the energy level diagram showing how the line spectra corresponding to Balmer series occur due to transition between energy levels.

Answer 1

Suppose m be the mass of an electron and v be its speed in nth orbit of radius r. The centripetal force for revolution is produced by electrostatic attraction between electron and nucleus.

Total energy,

Again from Bohr'* postulate for quantization of angular momentum.

Substituting value of rn in equation (ii), we get

R is called Rydberg constant.
For hydrogen atom Z =1,

En = - Rchn/n2

For Balmer series nf = 2, while ni = 3, 4, 5,...................∞