Zeke Says That the Magnitude of the Orbital Angular Momentum $\ell\hbar$

Multiple Choice

Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = $\ell\hbar$ .Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic field vector $\vec { B }$ is $\sqrt { \ell ( \ell + 1 ) } \hbar$ .Which one,if either,is correct,and why?

A) Ruth,because the maximum value of L is $\sqrt { \ell ( \ell + 1 ) } \hbar$ .
B) Ruth,because the orbital angular momentum always lines up with a magnetic field so that $\overrightarrow { \mathbf { L } }$ has its maximum value along the field.
C) Zeke,because the maximum magnitude of $\overrightarrow { \mathbf { L } }$ is L = $\ell\hbar$ .
D) Zeke,because the orbital angular momentum always lines up with a magnetic field so that $\overrightarrow { \mathbf { L } }$ has its maximum value along the field.
E) Neither,because they have interchanged the maximum magnitude of $\overrightarrow { \mathbf { L } }$ , $\sqrt { \ell ( \ell + 1 ) } \hbar$ ,and $\ell\hbar$ ,its maximum projection along a magnetic field direction.