(a) Using Bohr's second postulate of quantization of orbital angular momentum show that the circumference of the electron in the `n^(th)` 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 which it finally moves to the ground state ?

Explanation

(a) From de-Broglie hypothesis, wavelength associated with electron
`lamda=(h)/(mv) implies mv=(h)/(lamda)`
Substituting this value in `mv_(r )=n(h)/(2pi)`,
we get, `(h)/(lamda)r=n(h)/(2pi)`
`2pi r= n lamda`
i.e., circumference `(S=2pi r)` of nth permitted orbit for the electron can contain exactly n wavelength of de-Broglie wavelength associated with electron in that orbit. ?
(b) Number of spectral lines
`=(n(n-1))/(2)=(3(3-1))/(2)=(6)/(2)=3`.