Question

What are the values of orbital angular momentum of the electrons in the orbitals 1s, 3s, 3d and 2p ?

• A. 0, 0, $\sqrt{6}$ $\hslash$, $\sqrt{2}$ $\hslash$
• B. 1, 1, $\sqrt{4}$ $\hslash$, $\sqrt{2}$ $\hslash$
• C. 0, 1, $\sqrt{6}$ $\hslash$, $\sqrt{3}$ $\hslash$
• D. 0, 0, $\sqrt{20}\hslash$, $\sqrt{6}$ $\hslash$

Answer 1

The correct option is A 0, 0, $\sqrt{6}$ $\hslash$, $\sqrt{2}$ $\hslash$

$l$ is azimuthal quantum number.
$l$ = 0 $\to$ s subshell
$l$ = 1 $\to$ p subshell
$l$ = 2 $\to$ d subshell
$l$ = 3 $\to$ f subshell
Here, $\hslash$ $=$ $\frac{h}{2\pi }$
Orbital angular momentum $=$ $\sqrt{l(l+1)}\times \hslash$
For s subshell, $l$ $=$ 0, therefore for 1s and 3s
Orbital angular momentum =$\sqrt{l(l+1)}\times \hslash$ $=$ 0
For 3d, $l$ $=$ 2, therefore $\sqrt{l(l+1)}\times \hslash$ $=$ $\sqrt{2(2+1)}\times \hslash$ $=$ $\sqrt{6}\hslash$
For 2p, $l$ $=$ 1, therefore $\sqrt{1(1+1)}\times \hslash$ $=$ $\sqrt{1(1+1)}\times \hslash$ $=$ $\sqrt{2}\hslash$