Quantum Numbers

Quantum Numbers

The Three Physicists Louie de Broglie Erwin Schrodinger Werner Karl Heisenberg

Quantum Mechanical Model

The Quantum Mechanical Model ELECTRON CLOUDS

The probability of finding an electron in the region around the nucleus of an atom can be represented in many ways.

The Atom a.k.a The Condo SHELLS Energy levels

Number of sublevels in a main energy level is the same as the assigned main energy level.

Main Energy Level

Number of Sublevels

1 (lowest energy)

1

2

2

3

3

4

4

Main Energy Level

Kinds of Sublevels

1 (lowest energy)

1s

2

2s, 2p

3

3s, 3p, 3d

4

4s, 4p, 4d, 4f

5

5s, 5p, 5d, 5f, 5g

Sublevel

Number of Orbitals

s

1

p

3

d

5

f

7

g

9

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 4 Quantum Numbers Principal Quantum Number, n Azimuthal Quantum Number, l Magnetic Quantum Number, ml Spin Quantum Number, ms

Principal Quantum Number main energy level of an orbital. an increase in n also means increase in the energy of the electron in the orbital. n= 1, 2, 3…. maximum no. of orbitals = n2 maximum no. of electrons = 2n2

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

0

sharp - s

1

principal - p

2

diffused - d

3

fundamental f

Orbital Shape spherical dumbbellshaped cloverleaf too complex

Azimuthal Quantum Number A sublevel in a particular main energy level is defined by its n and its l values. n

l

1

0

Kind of Sublevel 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

Spin Quantum Number, ms spin of the electron values are +1/2 and -1/2 clockwise and counterclockwise opposite spins (Pauli Exclusion A – counterclockwise Principle). B – clockwise

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

Orbital Diagram

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

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 b. ml= -2, ms= +1/2 c. n=1, ml=+1 d. l=4, ml=-3 e. n=3, ms=0

Individual Assignment (due Thursday, Aug. 21) Answer Review p.91 letter C numbers 15 of your textbook in ½ crosswise. In your notebook, read electron configuration. Identify the 3 rules in writing electron configuration. Explain each.