The total number of electron states with n = 2 and for an atom is:
A) two
B) four
C) six
D) eight
E) ten

Question

The total number of electron states with n = 2 and  for an atom is:
A) two 
B) four 
C) six 
D) eight 
E) ten

Quizplus · Accepted Answer

According to the Pauli exclusion principle, no two electrons in an atom can have the same set of four quantum numbers. The quantum numbers of an electron are n (the principal quantum number), l (the azimuthal quantum number), ml (the magnetic quantum number), and ms (the spin quantum number).
For n = 2, the possible values of l are 0 and 1. When l = 0, there is one possible value of ml (0), and when l = 1, there are three possible values of ml (-1, 0, and 1). Each electron can have two possible values of ms (+1/2 or -1/2).
Therefore, the total number of possible electron states with n = 2 is 2 (for l = 0, ml = 0, and ms = +1/2 or -1/2) + 6 (for l = 1, ml = -1, 0, or 1, and ms = +1/2 or -1/2) = 8. 
Only choice C matches this number.

The Total Number of Electron States with N = 2