Question

The spin angular momentum for the ${}^{\prime }{s}^{\prime }$ electron in $H-atom$ is:

• A. $\frac{\sqrt{3}h}{4\pi }$
• B. $\sqrt{h}2\pi$
• C. $\sqrt{h}4\pi$
• D. $\frac{\sqrt{3}h}{2\pi }$

Answer 1

The correct option is A $\frac{\sqrt{3}h}{4\pi }$

The electronic configuration of hydrogen atom is $1s^1$.
So the total spin quantum number $S=\frac{1}{2}$
$\therefore$ Spin angular momentum $=\sqrt{S(S+1)}\frac{h}{2\pi }=\sqrt{\frac{1}{2}(\frac{1}{2}+1)}\frac{h}{2\pi }=\frac{\sqrt{3}h}{4\pi }$