Question

(a) State Bohr's postulate to define stable orbits in hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the $n=4$ level. Estimate the frequency of the photon.

Answer 1

A) Bohr's Postulates

1. An atom has a number of stable orbits in which an electron can reside without the emission of radiant energy. Each orbit corresponds, to a certain energy level.

2. An electron may jump spontaneously from one orbit (energy level $E_1$) to the other orbit (energy level $E_2$)($E_2>E_1$); then the energy change AE in the electron jump is given by Planck's equation

$\Delta E=E_2-E_1=hv$

3. The motion of an electron in a circular orbit is restricted in such a manner that its angular momentum is an integral multiple of $\frac{h}{2\pi }$

4. A special surface around the nucleus which contained orbits of equal energy and radius was called the shell. These shells are numbered from inside to outwards as 1, 2, 3, 4 etc. and called K, L, M, N respectively.

B. $\frac{1}{\lambda }=R_H[\frac{1}{1^2}-\frac{1}{4^2}]$

$\lambda =\frac{16}{15R_H}$

$Frequency=\frac{c}{\lambda }$

so $f=2.8\times {10}^{15}Hz$