Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom.
The four quantum numbers, the principal quantum number ( n ) , the angular momentum quantum number ( ) , the magnetic quantum number ( m ) , and the spin quantum number ( m s ) have strict rules which govern the possible values.
1. Identify all allowable combinations of quantum numbers for an electron.
a) n = 6 , = 6 , m = 0 , m s = + 1/2
b) n = 3 , = 2 , m = 1 , m s = − 1/2
c) n = 2 , = 0 , m = 0 , m s = 0
d) n = 3 , = − 2 , m = 1 , m s = − 1/2
e) n = 5 , = 4 , m = − 4 , m s = − 1/2
f) n = 4 , = 3 , m = 4 , m s = − 1/2