Question

An electron is in an angular momentum state with ℓ = 2.

a) What is the magnitude of the electron’s angular momentum vector?

b) How many different possible z components can the angular momentum vector have? List the possible z components.

c) What are the values of the angle that the L vector makes with the z axis?

Answer 1

a) The magnitude of the electron’s angular momentum vector:

$$L_l=\sqrt{l(l+1)}ħ=2.58\cdot10^{-34}\text{ m}^2\text{kg/s}.$$

b) The angular momentum may have 5 possible components that correspond to $m_l=0,\pm1,\pm2.$

c) The angle is

$$\theta=\text{arccos}\frac{\textbf{L}_z}{\textbf{L}}=\text{arccos}\frac{2}{\sqrt{2(2+1)}}=35°.$$