Question

How many states are possible for a given set of quantum numbers? For instance, n=1 means that l=0 with ml=0 are the only possible values for those variables. Thus, there are two possible states: (1, 0, 0, 1/2) and (1, 0, 0, −1/2). How many states are possible for n=2?

Answer 1

There are 8 possible states.

Explanation:

The principal quantum number (n) can take positive integer values. In this case, n = 2.

The angular quantum number (l) can take values from 0 to n - 1. In this case, l can take the values 0 and 1.

The magnetic quantum number (ml) can take values from -l to +l. When l is 0, ml can take the value 0. When l is 1, ml can take the values -1, 0 and 1.

The spin number (ms) can take the values +1/2 and -1/2.

All in all, all the possible combinations of n, l, ml and ms for n = 2 are:

2, 0, 0, -1/2

2, 0, 0, +1/2

2, 1, -1, -1/2

2, 1, -1, +1/2

2, 1, 0, -1/2

2, 1, 0, +1/2

2, 1, 1, -1/2

2, 1, 1, +1/2