What is the full multiplicity (number of states) of the n = 3 level of the H atom?
A) 18
B) 30
C) 16
D) 32
E) 9

Question

Quizplus · Accepted Answer

The full multiplicity of the n = 3 level of the hydrogen atom is calculated by considering the possible values of the angular momentum quantum number l (which can be 0, 1, or 2 for n = 3) and the magnetic quantum number m, which ranges from -l to +l for each value of l. For l = 0, there is 1 state; for l = 1, there are 3 states (m = -1, 0, +1); and for l = 2, there are 5 states (m = -2, -1, 0, +1, +2). Additionally, each of these states can have two possible spin orientations (spin up or spin down), doubling the total number. Thus, the total number of states is 2*(1 + 3 + 5) = 18.

What Is the Full Multiplicity (Number of States) of the N