Question

In $\Psi_{321}$ the sum of angular momentum, spherical nodes and angular node is :-

• A. $\frac{\sqrt{6} h + 4 \pi }{2 \pi }$
• B. $\frac{\sqrt{6} h}{2 \pi }+3$
• C. $\frac{\sqrt{6} h + 2 \pi }{2 \pi }$
• D. $\frac{\sqrt{6} h + 8 \pi }{2 \pi }$

Answer 1

Answer: (A)

$\psi_{321}\Rightarrow n=3,\ell =2,m=1$
angular momentum $=\frac{h}{2 \pi }\sqrt{\ell \left(\right. \ell + 1 \left.\right)}=\frac{\sqrt{6} h}{2 \pi }$
spherical node $=n-\ell -1$
$=3-2-1=0$
Angular node $=\ell =2$
sum $\Rightarrow \frac{\sqrt{6} h}{2 \pi }+0+2$
$\Rightarrow \frac{\sqrt{6} h + 4 \pi }{2 \pi }$