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Chapter 4

Quantum Numbers

Principal quantum number – ( n )

Angular momentum quantum number – ( l)

Magnetic quantum number – ( ml)

Spin quantum number – ( ms)

n=2

n=3

Quantum Numbers (n, l, ml, ms)principal quantum numbern

n= 1, 2, 3, 4, ….

distance of e- from the nucleus

Quantum Numbers(n, l, ml, ms)

angular momentum quantum numberl

for a given value of n,l= 0, 1, 2, 3, … n-1

l = 0 s orbital

l = 1 p orbital

l = 2 d orbital

l = 3 f orbital

n = 1, l = 0

n = 2, l = 0 or 1

n = 3, l = 0, 1, or 2

Shape of the “volume” of space that the e- occupies

l= 0 (s orbitals)

l= 1 (p orbitals)

l= 2 (d orbitals)

Quantum Numbers (n, l, ml, ms)

magnetic quantum numberml

for a given value of lml= -l, …., 0, …. +l

for l = 0 (s orbital)ml= 0

if l = 1 (p orbital),ml= -1, 0, or +1

if l = 2 (d orbital),ml= -2, -1, 0, +1, or +2

orientation of the orbital in space

Quantum Numbers (n, l, ml, ms)

spin quantum numberms

ms= +½or -½

ms = +½

ms = -½

Experimental arrangement for demo the spinning motion of electrons

Q & A

Quantum Numbers (n, l, ml, ms)

Existence (and energy) of electron in atom is described

by its unique Quantum Numbers

Pauli exclusion principle

No two electrons in an atom

can have the same four quantum numbers.

How many electrons can an orbital hold?

Quantum Numbers (n, l, ml, ms)

Shell – electrons with the same value of n

Subshell – electrons with the same values of nandl

Orbital – electrons with the same values of n, l, andml

How many electrons can be placed in the 3d subshell?

How many 2p orbitals are there in an atom?

Q & A

in the orbital or subshell

principal quantum

number n

angular momentum

quantum number l

1s1

Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom.

1s1

Orbital diagram

H

Order of orbitals (filling) in multi-electron atom

“Fill up” electrons in lowest energy orbitals (Aufbau principle)

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule).

Ne 10 electrons

Ne 1s22s22p6

F 9 electrons

F 1s22s22p5

O 8 electrons

O 1s22s22p4

N 7 electrons

N 1s22s22p3

What is the electron configuration of Mg? one with the greatest number of parallel spins

What are the possible quantum numbers for the last (outermost) electron in Cl?

Outermost subshell being filled with electrons one with the greatest number of parallel spins

2p one with the greatest number of parallel spins

2p

Paramagnetic

Diamagnetic

unpaired electrons

all electrons paired

Q & A session one with the greatest number of parallel spins

Name the orbital described by the following quantum numbers :

- n = 3, l = 0
- n = 3, l = 1
- n = 3, l = 2
- n = 5, l = 0

Q & A session one with the greatest number of parallel spins

Give the n and l values for the following orbital

a. 1s b. 3s c. 2p d. 4d e. 5f

What and the possible ml values for the following types of orbital?

a. s b. p c. d d. f

Q & A session one with the greatest number of parallel spins

How many possible orbital are there for n =

a. 4 b. 10

How many electrons can inhabit all of the n = 4 orbital?

Place the following orbital in order of increasing energy:

1s, 3s, 4s, 6s, 3d, 4f, 3p, 7s, 5d, 5p

Q & A session one with the greatest number of parallel spins

Write electron configurations for the following atoms:

a. H

b. Li+

c. N

d. F-

e. Ca

Q & A session one with the greatest number of parallel spins

Draw an orbital diagrams for atoms with the following electron configurations:

1s22s22p63s23p3

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