Physics 102: Lecture 25, Slide 1

Periodic Table, Atomic Structure

• Today’s Lecture will cover Section 28.7

Physics 102: Lecture 25

Make sure your grade book entries are correct.

Quantum NumbersEach electron in an atom is labeled by 4 #’sn = Principal Quantum Number (1, 2, 3, …)

• Determines energy

ms = Spin Quantum Number (+½ , -½)• “Up Spin” or “Down Spin”

ℓ = Orbital Quantum Number (0, 1, 2, … n-1)• Determines angular momentum•

mℓ = Magnetic Quantum Number (ℓ , … 0, … -ℓ )• Component of ℓ •

( 1)2hL

2zhL m

Physics 102: Lecture 25, Slide 3

Preflight 25.1

For which state of hydrogen is the orbital angular momentum required to be zero?

n=3 n=2 n=1

Physics 102: Lecture 25, Slide 4

Preflight 25.1

For which state of hydrogen is the orbital angular momentum required to be zero?

n=3 n=2 n=1

The allowed values of ℓ are 0, 1, 2, …, n-1. When n=1, ℓ must be zero.

Physics 102: Lecture 25, Slide 5

ℓ =0 is “s state”ℓ =1 is “p state”ℓ =2 is “d state”ℓ =3 is “f state”ℓ =4 is “g state”

1 electron in ground state of Hydrogen:

Nomenclature “Subshells”“Shells”

n=1 is “K shell”n=2 is “L shell”n=3 is “M shell”n=4 is “N shell”n=5 is “O shell”

Physics 102: Lecture 25, Slide 6

ℓ =0 is “s state”ℓ =1 is “p state”ℓ =2 is “d state”ℓ =3 is “f state”ℓ =4 is “g state”

1 electron in ground state of Hydrogen: n=1, ℓ =0 is denoted as: 1s1

n=1 ℓ =0 1 electron

Nomenclature “Subshells”“Shells”

n=1 is “K shell”n=2 is “L shell”n=3 is “M shell”n=4 is “N shell”n=5 is “O shell”

Physics 102: Lecture 25, Slide 7

Quantum NumbersHow many unique electron states exist with n=2?

Physics 102: Lecture 25, Slide 8

Quantum NumbersHow many unique electron states exist with n=2?

ℓ = 0 :mℓ = 0 : ms = ½ , -½ 2 statesℓ = 1 :mℓ = +1: ms = ½ , -½ 2 statesmℓ = 0: ms = ½ , -½ 2 statesmℓ = -1: ms = ½ , -½ 2 states

2s2

2p6

There are a total of 8 states with n=2

Physics 102: Lecture 25, Slide 9

ACT: Quantum NumbersHow many unique electron states exist with n=5 and ml = +3?

Physics 102: Lecture 25, Slide 10

ACT: Quantum NumbersHow many unique electron states exist with n=5 and mℓ = +3?

ℓ = 0 : mℓ = 0ℓ = 1 : mℓ = -1, 0, +1

There are a total of 4 states with n=5, mℓ = +3

ℓ = 2 : mℓ = -2, -1, 0, +1, +2ℓ = 3 : mℓ = -3, -2, -1, 0, +1, +2, +3

ms = ½ , -½ 2 statesℓ = 4 : mℓ = -4, -3, -2, -1, 0, +1, +2, +3, +4

ms = ½ , -½ 2 states

Onlyℓ = 3 and ℓ = 4have mℓ = +3

Physics 102: Lecture 25, Slide 11

In an atom with many electrons only one electron is allowed in each quantum state (n, ℓ,mℓ,ms).

Pauli Exclusion Principle

This explains the periodic table!

Physics 102: Lecture 25, Slide 12

Preflight 25.2What is the maximum number of electrons that can exist in the 5g (n=5, ℓ = 4) subshell of an atom?

Physics 102: Lecture 25, Slide 13

Preflight 25.2What is the maximum number of electrons that can exist in the 5g (n=5, ℓ = 4) subshell of an atom?

mℓ = -4 : ms = ½ , -½ 2 statesmℓ = -3 : ms = ½ , -½ 2 states mℓ = -2 : ms = ½ , -½ 2 statesmℓ = -1 : ms = ½ , -½ 2 statesmℓ = 0 : ms = ½ , -½ 2 statesmℓ = +1: ms = ½ , -½ 2 statesmℓ = +2: ms = ½ , -½ 2 statesmℓ= +3: ms = ½ , -½ 2 statesmℓ = +4: ms = ½ , -½ 2 states

18 states

Physics 102: Lecture 25, Slide 14

Atom Configuration H 1s1

He 1s2

Li 1s22s1

Be 1s22s2

B 1s22s22p1

Ne 1s22s22p6

1s shell filled

2s shell filled

2p shell filled etc

(n=1 shell filled - noble gas)

(n=2 shell filled - noble gas)

Electron Configurations

p shells hold up to 6 electronss shells hold up to 2 electrons

Physics 102: Lecture 25, Slide 15

2s electrons can get closer to nucleus, which means less “shielding” from the 1s electrons

Shell OrderingWhy do s shells fill first before p?

r

2p

P(r)

r

2s

P(r)1s 1s

Physics 102: Lecture 25, Slide 16

Sequence of shells: 1s,2s,2p,3s,3p,4s,3d,4p…..4s electrons get closer to nucleus than 3d

24 Cr

26 Fe

19K

20Ca

22 Ti

21Sc

23 V

25 Mn

27 Co

28 Ni

29 Cu

30 Zn

4s3d 4p

In 3d shell we are putting electrons into ℓ = 2; all atoms in middle are strongly magnetic.

Angular momentum

Loop of current

Large magnetic moment

Sequence of Shells

Physics 102: Lecture 25, Slide 17

Yellow line of Na flame test is 3p

3s

Na 1s22s22p6 3s1

Neon - like core

Many spectral lines of Na are outer electron making transitions

Single outer electron

Sodium

www.WebElements.com

Physics 102: Lecture 25, Slide 18

Summary• Each electron state labeled by 4 numbers:

n = principal quantum number (1, 2, 3, …)ℓ = angular momentum (0, 1, 2, … n-1)mℓ = component of ℓ (-ℓ < mℓ < ℓ)

ms = spin (-½ , +½)

• Pauli Exclusion Principle explains periodic table• Shells fill in order of lowest energy.

Physics 102: Lecture 25, Slide 19

See you later!

• Read Textbook Section 27.4

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