Question

The ratio of angular momentum in $3$rd orbit and orbital angular momentum of $3d$-orbital is:

• A. $\sqrt{6}$
• B. $\sqrt{\frac{3}{2}}$
• C. $\sqrt{\frac{2}{3}}$
• D. $\frac{1}{\sqrt{6}}$

Answer 1

Answer: (B)

$\sqrt{\frac{3}{2}}$

As we know,
Angular momentum in $3$rd orbit$P_1=\frac{nh}{2\pi }=\frac{3}{2}\frac{h}{\pi }$
Angular momentum in $3d$-orbital ($l=2$ for d-orbitals)
$P_2=\frac{h}{2\pi }\sqrt{l(l+1)}=\frac{h}{2\pi }\times \sqrt{6}$
So
$P_1/P_2=\frac{3}{2}\times \frac{2}{\sqrt{6}}=\sqrt{\frac{3}{2}}$