Periodic Table, Atomic Structure

Physics 102: Lecture 25

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Quantum NumbersEach electron in an atom is labeled by 4 #’s

n = Principal Quantum Number (1, 2, 3, …)

• Determines energy (Bohr)

ms = Spin Quantum Number (-½ , +½)

• “Up Spin” or “Down Spin”

l = Orbital Quantum Number (0, 1, 2, … n-1)

• Determines angular momentum• l < n always true!

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

• Component of l • | ml | <= l always true!

( 1)2

hL

2z

hL m

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ACT

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

1. n=1

2. n=2

3. n=3

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

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75%

15%

10%

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”

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Quantum Numbers

How many unique electron states exist with n=2?

l = 0 :ml = 0 : ms = ½ , -½ 2 states

l = 1 :ml = +1: ms = ½ , -½ 2 states

ml = 0: ms = ½ , -½ 2 states

ml = -1: ms = ½ , -½ 2 states

2s2

2p6

There are a total of 8 states with n=216

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

l = 0 : ml = 0

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

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

+3

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

l = 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 = 4

have ml = +3

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A) 0 B) 4 C) 8 D) 16 E) 50

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!

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Preflight 25.2

What 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 states

ml = -3 : ms = ½ , -½ 2 states

ml = -2 : ms = ½ , -½ 2 states

ml = -1 : ms = ½ , -½ 2 states

ml = 0 : ms = ½ , -½ 2 states

ml = +1: ms = ½ , -½ 2 states

ml = +2: ms = ½ , -½ 2 states

ml = +3: ms = ½ , -½ 2 states

ml = +4: ms = ½ , -½ 2 states

18 states2*9

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in general, 2*(2l+1)

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 electrons29

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)1s1s

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Sequence of shells: 1s,2s,2p,3s,3p,4s,3d,4p…..

4s electrons get closer to nucleus than 3d

Sequence of Shells

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1s2p3p4p5p

4f5f

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

4s

3d 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

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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

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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.

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