Question

(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 when it finally moves to the ground state?

Answer 1

(A)Postulate of quantization of orbital angular momentum states

$mvr=\frac{nh}{2\pi }$

$⟹2\pi r=\frac{nh}{mv}$

The left hand side is the circumference of the electron in $n^{th}$ orbital, and right hand side is the $n$ times the wavelength associated with atom in $n^{th}$ state($\frac{h}{mv}$).

(B) The atom in $n=3$ could jump back to $n=2$ . After jumping to $n=2$ it could further jump to $n=1$.
Hence possible spectrum lines are three corresponding to

$n=3\to n=1$

$n=3\to n=2$

$n=2\to n=1$