Question

The orbital angular momentum of an electron is $\sqrt{3}\frac{h}{\pi }$. Which of the following may be a permissible value of angular momentum of an electon revolving in an unknown Bohr's orbit?

• A. $\frac{h}{\pi }$
• B. $\frac{h}{2\pi }$
• C. $\frac{3h}{2\pi }$
• D. $\frac{2h}{\pi }$

Answer 1

The correct option is D $\frac{2h}{\pi }$

Given orbital angular momentum = $\sqrt{3}\frac{h}{\pi }$

We know that orbital anugular momentum of an orbital is given by $\sqrt{l(l+1)}\frac{h}{2\pi }$
On equating both we get,$\sqrt{l(l+1)}\frac{h}{2\pi }=\sqrt{3}\frac{h}{\pi }$
From here, $l(l+1)=12$
$\therefore l=-4,3$ (But -4 is not allowed as value of l cannot be negative).
Hence, l = 3 is final accepted value.
Hence possible values of n = $4,5,6$

We also know that according to Bohr's model angular momentum for an orbit is given by $mvr=\frac{nh}{2\pi }$

Thus, possible angular momentum values can be $\frac{4h}{2\pi },\frac{5h}{2\pi },\frac{6h}{2\pi }$.
Hence as per the given options, D is the correct answer.