Zeke Says That the Magnitude of the Orbital Angular Momentum

Multiple Choice

Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = . Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic field vector is . Which one, if either, is correct, and why?

A) Ruth, because the maximum value of L is
.
B) Ruth, because the orbital angular momentum always lines up with a magnetic field so that
has its maximum value along the field.
C) Zeke, because the maximum magnitude of
is L =
.
D) Zeke, because the orbital angular momentum always lines up with a magnetic field so that
has its maximum value along the field.
E) Neither, because they have interchanged the maximum magnitude of
,
, and
, its maximum projection along a magnetic field direction.