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. Identify all allowable combinations of quantum numbers for an electron. n = 4 , ???? = 2 , m ???? = 3 , m s = − 1 2 n = 2 , ???? = 1 , m ???? = − 1 , m s = 0 n = 5 , ???? = 5 , m ???? = 1 , m s = + 1 2 n = 5 , ???? = 2 , m ???? = 1 , m s = + 1 2 n = 3 , ???? = − 2 , m ???? = − 1 , m s = + 1 2 n = 3 , ???? = 2 , m ???? = − 1 , m s = − 1 2

The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number ( ml), and the spin quantum number ( ms ) have strict rules which govern the possible values.

Identity allowable combinations of quantum numbers for an electron. Select all that apply.

The rules that govern the possible values for the quantum numbers are:

The principal quantum number (n) can take positive integer values (1, 2, 3...)
The angular momentum quantum number (l) can take values from 0 to n-1.
The magnetic quantum number ( ml) can take values from -l to +l.
The spin quantum number ( ms ) can take the values -1/2 and +1/2.

a) n = 4 , l = 2 , ml = 3 , ms = − 1/2. NOT ALLOWABLE. If l = 2, ml cannot be 3.

b) n = 2 , l = 1 , ml = − 1 , ms = 0. NOT ALLOWABLE. ms cannot take the value 0.

c) n = 5 , l = 5 , ml = 1 , ms = + 1/2. NOT ALLOWABLE. If n = 5, l cannot be 5.

d) n = 5 , l = 2 , ml = 1 , ms = + 1/2. ALLOWABLE.

e) n = 3 , l = − 2 , ml = − 1 , ms = + 1/2. NOT ALLOWABLE. l cannot take negative values.

f) n = 3 , l = 2 , ml = − 1 , ms = − 1/2. ALLOWABLE.