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”

D-orbital

• With 5 different orientations

http://www.crystalstructures.com/IMAGES/Orbital-Dyz.jpg

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