Question

The orbital angular moments of an electron is $\sqrt{3}\frac{h}{\pi }$.Which of the following may be the permissible value of angular momentum of this electron revolving in an unknown 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 $\frac{2h}{\pi }$

$\begin{array}{c}\text{Given: orbital angular momentum,}\\ \begin{array}{cc}\sqrt{l(l+1)}\frac{h}{2\pi }=\sqrt{3}\frac{h}{\pi }& \\ \frac{l(l+1)}{4}& =3\\ \ell (l+1)& =3(3+1)\\ \therefore & l=3\end{array}\end{array}$

$\begin{array}{c}\text{since,}l=3\\ \text{permissible values of}n\text{are}4,5,6,\dots .\\ \text{Angular momentum can be}\frac{2h}{\pi }\text{,}\frac{5h}{2\pi },\frac{3h}{\pi }\text{,}\dots \\ \therefore \frac{2h}{\pi }\end{array}$