Electrons can be labelled using the subshell and orbital or by using the four quantum numbers:
n : principal quantum number
l : azimuthal quantum number
ml : magnetic quantum number
ms : spin quantum number
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.
The maximum number of subshells permitted for a particular shell is equal to n2.
The maximum number of electrons permitted in a particular shell is equal to 2 x n2.
n
Energy Level
Shell
No. Subshells = n2
No. electrons = 2n2
1
1st energy level
K
1
2
2
2nd energy level
L
4
8
3
3rd energy level
M
9
18
4
4th 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.
l can have values ranging from 0 to n-1.
The number of orbitals permitted for a particular subshell is equal to 2l + 1.
value of n
l = n - 1
subshell (orbital shape)
No. orbitals = 2l + 1
1
0
s subshell
1 (1 x s orbitals)
2
1
p subshell
3 (3 x p orbitals)
3
2
d subshell
5 (5 x d orbitals)
4
3
f subshell
7 (7 x f orbitals)
Magnetic Quantum Number, ml
The magnetic quantum number, ml, tells us the orientation of an orbital in space.
ml can have values ranging from -l to +l.
It is not always possible to associate a value of ml with a particular orbital.
value of l
subshell
values of ml
possible orbitals
0
s
0
s
1
p
-1, 0, 1
px, py, pz
2
d
-2, -1, 0, 1, 2
dxy, dxz, dyz, dx2-y2, dz2
3
f
-3, -2, -1, 0, 1, 2, 3
Spin Quantum Number, ms
The spin quantum number, ms, tells us the spin of the electron.
ms can have a value of +½ or -½.
Example
The argon atom has 18 electrons.
The quantum numbers for each of the 18 electrons is shown below:
electron
n (shell)
l (subshell)
ml (possible orbital)
ms
1
1 (K)
0 (s)
0 (1s)
-½
2
1 (K)
0 (s)
0 (1s)
+½
3
2 (L)
0 (s)
0 (2s)
-½
4
2 (L)
0 (s)
0 (2s)
+½
5
2 (L)
1 (p)
-1 (2px)
-½
6
2 (L)
1 (p)
-1 (2px)
+½
7
2 (L)
1 (p)
0 (2py)
-½
8
2 (L)
1 (p)
0 (2py)
+½
9
2 (L)
1 (p)
+1 (2pz)
-½
10
2 (L)
1 (p)
+1 (2pz)
+½
11
3 (M)
0 (s)
0 (3s)
-½
12
3 (M)
0 (s)
0 (3s)
+½
13
3 (M)
1 (p)
-1 (3px)
-½
14
3 (M)
1 (p)
-1 (3px)
+½
15
3 (M)
1 (p)
0 (3py)
-½
16
3 (M)
1 (p)
0 (3py)
+½
17
3 (M)
1 (p)
-1 (3pz)
-½
18
3 (M)
1 (p)
-1 (3pz)
+½
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