An atom has completely filled inner shells and a single valence electron in an excited $p$ state. The filled inner shells have an orbital momentum equal to zero. When a magnetic field is applied, what are the possible angles between the magnetic field and the orbital angular momentum?
A) $45 ^ { \circ } , 90 ^ { \circ } , 135 ^ { \circ }$
B) $45 ^ { \circ } , 90 ^ { \circ }$
C) $45 ^ { \circ } , 135 ^ { \circ }$
D) $90 ^ { \circ }$
E) $45 ^ { \circ }$

Question

Quizplus · Accepted Answer

The orbital angular momentum of a single electron in a $p$ state is $ \hbar $. When a magnetic field is applied, the electron's magnetic moment will align with the field, resulting in a precession of the electron's orbital angular momentum around the field. The possible angles between the magnetic field and the orbital angular momentum are given by the equation $ \cos \theta = \frac { m _ { l } } { l } $, where $ m _ { l } $ is the magnetic quantum number and $ l $ is the orbital angular momentum quantum number. For a single electron in a $p$ state, $ l = 1 $ and $ m _ { l } = -1, 0, 1 $. Therefore, the possible angles between the magnetic field and the orbital angular momentum are $ \theta = 45 ^ { \circ } , 90 ^ { \circ } , 135 ^ { \circ } $.

An Atom Has Completely Filled Inner Shells and a Single ppp

An Atom Has Completely Filled Inner Shells and a Single $p$