Quantum Numbers
The Three Physicists
Louie de BroglieErwin Schrodinger
Werner Karl Heisenberg
Quantum Mechanical Model
Quantum mechanics
• examines the wave motion of objects
Atomic orbital
• Specified by three quantum numbers
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.
The 3 Quantum Numbers
Principal Quantum Number, n
Azimuthal Quantum Number, l
Magnetic Quantum Number, ml
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….
Azimuthal Quantum Number
also called Angular Momentum Number
defines the shape of the orbital.
values range from 0 to n-1.l = n - 1
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
S- orbital
• Spherical shape with the nucleus at its center
P-orbital
• “dumb-bell shape”
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
Magnetic Quantum Number, ml
describes the orientation of the orbital in space.
values are –l to +l
values per sublevel = 2l +1.
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
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 22s2p
13
26
3 33s3p3d
135
26
10
4 4
4s4p4d4f
1357
26
1014
Orbital Diagram
Exercise No. 1Quantum 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 orbitalb. 4d orbital
Give the quantum numbers in:a. 4f3
b. 3p5
Exercise No. 2Quantum Numbers
Which of the following sets of QN is NOT possible? Write possible or impossible and justify your answer.
a. n=2, l=1c. n=1, ml=+1
d. l=4, ml=-3
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