For the angular momentum vector corresponding to the quantum number $l$ = 3, the angle between the z axis when m = 2 is
A) 55°.
B) 45°.
C) 35°.
D) 25°.

Question

Quizplus · Accepted Answer

The angle $\theta$ between the angular momentum vector and the z-axis for a given quantum number $l$ and magnetic quantum number $m$ can be calculated using the relation $\cos(\theta) = \frac{m}{\sqrt{l(l+1)}}$. For $l = 3$ and $m = 2$, $\cos(\theta) = \frac{2}{\sqrt{3(3+1)}} = \frac{2}{\sqrt{12}} = \frac{1}{\sqrt{3}}$, which corresponds to an angle of approximately 55°.

For the Angular Momentum Vector Corresponding to the Quantum Number lll

For the Angular Momentum Vector Corresponding to the Quantum Number $l$