Question

Consider the following combinations of quantum numbers describing an electron in a hydrogen atom. Which combinations are allowed?

N L mi m Allowed or forbidden? If forbidden, give reason(s):
1 0 0 1
1 3 3 1/2
3 2 3 -1/2
0 1 0 1/2
2 1 -1 0
2 -1 -1 1/2

Answer 1

1 0 0 1- forbidden

1 3 3 1/2- forbidden

3 2 3 -1/2- forbidden

0 1 0 1/2- forbidden

2 1 -1 0- forbidden

2 -1 -1 1/2- forbidden

Step-by-step explanation:

1 0 0 1 is a forbidden combination because the spin quantum number can only take values of ±1/2.

1 3 3 1/2 is forbidden because it refers to an electron in a 1f orbital which does not exist.

3 2 3 -1/2 refers to an electron in a 3d orbital. However, the allowed values of the magnetic quantum number are only -2,-1,0,1,2. Hence 3d orbital cannot have a magnetic quantum number of 3.

No electron can be found in an n=0 energy level hence 0 1 0 1/2 does not exist.

Given 2 1 -1 0, the combination is forbidden because the allowed values of the spin quantum number are only ±1/2.

For 2 -1 -1 1/2, this combination is forbidden because the values of the orbital quantum number must be positive integers and not negative integers.