(a) Using Bohr's second postulate of quantization of orbital angular momentum, show that the circumference of the electron in the nth orbital state in hydrogen atom is n times the de-Broglie wavelength associated with it.
(b) The electron in hydrogen atom is initially in the third excited state. What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state ?

Explanation

According to Bohr.s second postulate
`mvr_(n)=(nh)/(2pi)`
`rArr 2pir_(n)=(nh)/(mv)`
But `(h)/(mv)=(h)/(p)= lambda`
But `(h)/(mv)=(h)/(p)=lambda`
`:. 2pi r_(n)=n lambda`
(b) For third excited state, `n=4`
for ground state `n=1`
Hence possible transitions are
`n_(f)=4 "to" n_(i)=3,2,1`
`n_(f)=3 "to" n_(i)=2,1`
`n_(f)=2"to" n_(i)=1`
otal number of transitions = 6