Question

The ratio of orbital angular momentum and spin angular momentum of an electron in $p$ orbital is:

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

Answer 1

The correct option is C $\frac{2\sqrt{2}}{\sqrt{3}}$

As we know,
For $p^1$ Orbital $l\left(\text{azimuthal quantum number}\right)=1$ and
$s\left(\text{spin quantum number}\right)=+1/2\text{or}-1/2$
$\frac{L\left(\text{orbital angular momentum}\right)}{S\left(\text{spin angular momentum}\right)}=\frac{\sqrt{l(l+1)}h/2\pi }{\sqrt{s(s+1)}h/2\pi }=\frac{\sqrt{2}}{\frac{\sqrt{3}}{2}}=\frac{2\sqrt{2}}{\sqrt{3}}$