Question

What is the angle made by angular momentum vector of an electron with $Z$ -axis?

• A. $cos\theta =l/m$
• B. $cos\theta =\sqrt{\frac{l}{m}}$
• C. $cos\theta =\frac{\sqrt{\left(l+1\right)}l}{m}$
• D. $cos\theta =\frac{m}{\sqrt{\left(l+1\right)}l}$

Answer 1

Answer: (D)

$Z$ component of the angular momentum $L_Z=\frac{mh}{2\pi }$
$L_Z=Lcos\theta =\sqrt{l\left(l+1\right)}cos\theta \frac{h}{2\pi }$
$\therefore \sqrt{l\left(l+1\right)}cos\theta =m$
or $cos\theta =\frac{m}{\sqrt{l\left(l+1\right)}}$