(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 then n = 4 level . Estimate the frequeny of the photon.

Explanation

(a) For stable orbit the angular momentum of revolving `e^(-2)` equal to `(nh)/(2pi)`
`mvr = (nh)/(2pi)`
According to de Broglie 's hypothesis,
`n lambda = al`
revolving `e^(-)` is stable orbit also associated with wave character. Hence, a cicular orbit can be taken to be stable orbit if it contains an integral number of de Broglie wavelenghts.
`2pi r = n lambda`
`2pir n((h)/(p))`
`pr = (nh)/(2pi)`
`mvr = (nh)/(2pi)` only a certain number of wavelenghts.
(b) For gound state `n_(1) = 1, n _(2) = 4`
Energy of photon absorbed.
`F = E_(2) - E_(1)`
`E_(1) = - 13.6//n_(12) = - 13.6eV`
`E_(2) = - 13.6//(n_(2))^(2) = 13.6//(4)^(2) = - 0.85eV`
The energy absorbed `= - 0.85 - (-13.6) = - 0.85 + 13.6 = 12.7 eV = 12.75 xx 1.6 xx 10^(-19)`
`= 20.4 xx 10^(-19)J`
Frequency , `V = C//lambda = 3 xx 10^(8)//9.7 xx 10^(-8) = 3.1 xx 10^(15) Hz`.