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?

There are 8 possible states.

Step-by-step 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