Quantum Numbers

How does a letter get to you?

5501 Haltom Rd

Haltom City, TX 76137

How does a letter get to you?

5501 Haltom Rd

Haltom City, TX 76137

Very general – includes many cities

How does a letter get to you?

5501 Haltom Rd

Haltom City, TX 76137

Very general – includes many cities

Still general – includes a handful of cities

How does a letter get to you?

5501 Haltom Rd

Haltom City, TX 76137

Very general – includes many cities

Still general – includes a handful of cities

Specific, but includes many places

How does a letter get to you?

5501 Haltom Rd

Haltom City, TX 76137

Very general – includes many cities

Still general – includes a handful of cities

Specific, but includes many places

Very specific – specifies only 1 place

Quantum numbers are mathematical “addresses” of electrons for an atom – no two electrons can have the same exact address

NotesSummary

Quantum numbers are mathematical “addresses” of electrons for an atom – no two electrons can have the same exact address

(n, l, ml, ms) => title

n = principle quantum number

•energy level

•relates to size

•possible values are all positive integers (1 to ∞)

•n = 1, 2, 3, 4, 5, 6, 7

(seven periods on the periodic table)

Notes

Summary

l = azimuthal quantum number

•sublevel

•relates to shape

•possible values are 0 to n-1 (currently 0-3)

s = 0

p = 1

d = 2

f = 3

Notes

Summary

ml = magnetic quantum number

•orbitals

•possible values are integers from –l to l

if l = 0 , then s = 0

if l = 1, then p = -1, 0, 1

if l = 2, then d = -2, -1, 0, 1, 2

if l = 3, then f = -3, -2, -1, 0, 1, 2, 3

Notes

Summary

ms = spin quantum number

•spin of the electron

•possible values are ½ and -½

= ½

= -½

Notes

Summary

example – Ti (22 electrons)

orbital notation

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

example – Ti (22 electrons)

orbital notation

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

1st arrow (1, 0, 0, ½)

example – Ti (22 electrons)

orbital notation

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

1st arrow (1, 0, 0, ½)

2nd arrow (1, 0, 0, -½)

example – Ti (22 electrons)

orbital notation

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

1st arrow (1, 0, 0, ½)

2nd arrow (1, 0, 0, -½)

Can be combined into (1, 0, 0, ±½)

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)

for 3s: (3, 0, 0, ±½)

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)

for 3s: (3, 0, 0, ±½)

for 3p: (3, 1, -1, ±½) and (3, 1, 0, ±½) and (3, 1, 1, ±½)

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)

for 3s: (3, 0, 0, ±½)

for 3p: (3, 1, -1, ±½) and (3, 1, 0, ±½) and (3, 1, 1, ±½)

for 4s: (4, 0, 0, ±½)

___ ___ ___ ___ ___ ___ ___ ___ __ ___ ___ ___ ___ ___ ___

1s 2s 2p 3s 3p 4s 3d

3rd and 4th arrows = (2, 0, 0, ±½)

for 2p: (2, 1, -1, ±½) and (2, 1, 0, ±½) and (2, 1, 1, ±½)

for 3s: (3, 0, 0, ±½)

for 3p: (3, 1, -1, ±½) and (3, 1, 0, ±½) and (3, 1, 1, ±½)

for 4s: (4, 0, 0, ±½)

for 3d: (3, 2, -2, ½) and (3, 2, -1, ½)

notice -- no more arrows