Question

An electron is in the n = 3 state. What is the smallest possible value for the angle between the z component of the orbital angular momentum and the orbital angular momentum?

Answer 1

The smallest value for $\theta$ corresponds to the largest value of cos $\theta$ .

Using

$cos\theta =\sqrt{\frac{l}{l+1}}$

For n = 3 largest allowed value of l = 2

hence

$cos\theta =\sqrt{\frac{2}{2+1}}=0.8165$

$\theta =35.26^{o}$