The document discusses quantum numbers which describe the properties of an electron in an atom. There are three main quantum numbers - the principal quantum number n, which indicates the main energy level; the azimuthal quantum number l, which defines the orbital shape; and the magnetic quantum number ml, which describes the orientation of the orbital. Together these quantum numbers uniquely specify each atomic orbital an electron can occupy. The document provides examples of the quantum numbers for different atomic orbitals and energy levels.

1. Quantum Numbers

2. The Three Physicists
Louie de Broglie
Erwin Schrodinger
Werner Karl Heisenberg
Quantum Mechanical Model

3. Quantum mechanics
• examines the wave motion of objects
Atomic orbital
• Specified by three quantum numbers

4. Quantum Numbers
According to Heisenberg’s Uncertainty
Principle, it is not possible to give the
exact position of an electron and its
energy at the same time.
But the probability of finding an electron
in an orbital of given energy can be
determined.

5. The 3 Quantum Numbers
Principal Quantum Number, n
Azimuthal Quantum Number, l
Magnetic Quantum Number, ml

6. Principal Quantum Number
main energy level of an orbital.
Indicates the relative size of the orbital
an increase in n also means increase in
the energy of the electron in the orbital.
n= 1, 2, 3….

7. Azimuthal Quantum Number
also called Angular Momentum Number
defines the shape of the orbital.
values range from 0 to n-1.
l = n - 1

8. Azimuthal Quantum Number
l Sublevel Orbital Shape
0 sharp - s spherical
1 principal - p
dumbbell-
shaped
2 diffused - d cloverleaf
3 fundamental - f too complex

10. S- orbital
• Spherical shape with the nucleus at its
center

11. P-orbital
• “dumb-bell shape”

12. D-orbital
• With 5 different orientations

14. Azimuthal Quantum Number
A sublevel in a particular main energy
level is defined by its n and its l values.
n l Kind of
Sublevel
1 0 1s
3 1 3p

15. Magnetic Quantum Number, ml
describes the orientation of the orbital in
space.
values are –l to +l
values per sublevel = 2l +1.

16. Magnetic Quantum Number, ml
Sublevel l ml
s 0 0
p 1 -1,0,+1
d 2 -2,-1,0,1,+2
f 3 -3,-2,-1,0,+1,+2,+3

17. Sublevel and Capacity of Each Main Energy
Level
Main
Energy
Level
No. of
Sublevel
Identity of
Sublevels
No. of
Orbitals
(n2)
Max. No. of
Electrons
(2n2)
1 1 1s 1 2
2 2
2s
2p
1
3
2
6
3 3
3s
3p
3d
1
3
5
2
6
10
4 4
4s
4p
4d
4f
1
3
5
7
2
6
10
14

18. Orbital Diagram

19. Exercise No. 1
Quantum Numbers
Give all the possible quantum numbers for
electrons in the 2nd energy level.
Give all the possible quantum numbers for
electrons in:
a. 3s orbital
b. 4d orbital
Give the quantum numbers in:
a. 4f3
b. 3p5

20. Exercise No. 2
Quantum Numbers
Which of the following sets of QN is NOT
possible? Write possible or impossible
and justify your answer.
a. n=2, l=1
c. n=1, ml=+1
d. l=4, ml=-3