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Principal Quantum Number, n
The principal quantum number, n, is always a positive integer and tells us the energy level or shell that the electron is found in.^{1}
The principal quantum number is essentially the same as the n of the Bohr model of the atom.
The maximum number of subshells permitted for a particular shell is equal to n^{2}.
If the principal quantum number is 1, n = 1, then the number of permitted energy sublevels (subshells) = 1^{2} = 1
That is, the first energy level (shell) has only one permitted energy sublevel (subshell).
If the principal quantum number is 2, n = 2, then the number of permitted energy sublevels (subshells) = 2^{2} = 4
That is, in the second energy level (shell) 4 sublevels (subshells) are permitted.
The maximum number of electrons permitted in a particular energy level (shell) is equal to 2 × n^{2}.
If the principal quantum number is 1, n = 1, then the maximum number of electrons permitted in this shell = 2 × 1^{2} = 2
That is, a maximum of 2 electrons can occupy the first energy level (shell).
If the principal quantum number is 2, n = 2, then the maximum number of electrons permitted in this shell = 2 × 2^{2} = 2 × 4 = 8
That is, a maximum of 8 electrons can occupy the second energy level (shell).
n 
Energy Level 
Shell 
No. Subshells = n^{2} 
No. electrons = 2n^{2} 
1 
1^{st} energy level 
K 
1 
2 
2 
2^{nd} energy level 
L 
4 
8 
3 
3^{rd} energy level 
M 
9 
18 
4 
4^{th} energy level 
N 
16 
32 
Azimuthal Quantum Number, l
The azimuthal quantum number tells us which subshell the electron is found in, and therefore it tells us the shape of the orbital.^{2}
l can have values ranging from 0 to n1.
If n = 1, l = 1  1 = 0
If n = 2, l = 2  1 = 1
The number of orbitals permitted for a particular subshell is equal to 2l + 1.
If l = 0, the number of permitted orbitals = 2 × 0 + 1 = 1
If l = 1, the number of permitted orbitals = 2 × 1 + 1 = 3
value of n 
l = n  1 
subshell (orbital shape) 
No. orbitals = 2l + 1 
1 
0 
s subshell 
1 (1 set of s orbitals) 
2 
1 
p subshell 
3 (3 sets of p orbitals) 
3 
2 
d subshell 
5 (5 sets of d orbitals) 
4 
3 
f subshell 
7 (7 sets of f orbitals) 
Magnetic Quantum Number, m_{l}
The magnetic quantum number, m_{l}, tells us the orientation of an orbital in space.
m_{l} can have values ranging from l to +l.
If l = 0, m_{l} = 0
If l = 1, m_{l} = 1, or, m_{l} = 0, or, m_{l} = +1
It is not always possible to associate a value of m_{l} with a particular orbital.
value of l 
subshell 
values of m_{l} 
possible orbitals 
0 
s 
0 
s 
1 
p 
1, 0, 1 
p_{x}, p_{y}, p_{z} 
2 
d 
2, 1, 0, 1, 2 
d_{xy}, d_{xz}, d_{yz}, d_{x2y2}, d_{z2 } 
3 
f 
3, 2, 1, 0, 1, 2, 3 

Spin Quantum Number, m_{s}
The spin quantum number, m_{s}, tells us the spin of the electron.
m_{s} can have a value of +½ or ½.