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Chem 1 Ch 4 Notes – Quantum Numbers
Quantum Numbers
1. n = principal quantum number
n = the main energy level ( the row on the periodic table)
n = 1,2,…7
2.  = angular momentum quantum number (azimuthal q.n. or subsidiary q.n.)
 = shape of orbital
 = 0…n-1 (0=s, 1=p, 2=d, 3=f)
3. m= magnetic quantum number (magnetic angular momentum q.n.)
= orientation in space
= - , … 0…, 
 There are 2n-1 orientations available for each main energy level.
4. ms = spin quantum number (magnetic spin q.n.)
= up or down spin
= +1/2 or -1/2 (or +h/2 , -h/2)
There are n different orbitals allowed for each main energy level:
n=1
s
= 0
n=2
s, p
 = 0, 1
n=3
s, p, d
 = 0, 1, 2
n=4
s, p, d, f
 = 0, 1, 2, 3
There are 2n-1 orientations available for each main energy level (n):
n
2n-1
m= - , … 0…, 
1
1 (2*1-1)
0 → only 1 s-orbital
2
3 (2*2-1)
-1, 0, 1 → 3 p-orbitals
3
5 (2*3-1)
-2, -1, 0, 1, 2 → 5 d-orbitals
4
7 (2*4-1)
-3, -2, -1, 0, 1, 2, 3 → 7 f-orbitals
There are n2 total orbitals for each main energy level:
There are 2n2 electrons per main energy level (2 electrons per orbital):
n
n2
2n2
1
1
1(s)
2
2
4
1(s) + 3(p) = 4 total orbitals
8
3
9
1 + 3 + 5(d) = 9 total orbitals
18
4
16
1 + 3 + 5 + 7(f) = 16 total orbitals
32