How many different quantum states are there in the Hydrogen atom with principal quantum number n = 5?

Question

How many different quantum states are there in the Hydrogen atom with principal quantum number n = 5 and orbital quantum number l = 2?

There are __?__ quantum states with these quantum numbers.

Select the range of magnetic quantum numbers ml that are allowed in this case, by selecting the lowest and highest allowed values from the list below.

(each ? should be over a negative or positive nr)

? ? ? ? ? ? ? ? ? ? ? ? ?

-6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6

Answer 1

For any n, el ranges from 0 to n-1, and m(el) ranges from -el to +el.

In this case, you are told that el = 2, so use what I just said to find range of m(el).

Hint: el = 0, s; el =1, p; el = 2, d.