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 }

\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.

In an Atom That Has an Electron in a Sub-Shell ℓ\ellℓ

Multiple Choice