Quantum Numbers Key Concepts
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 - 1subshell 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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