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Physics 102: Lecture 25, Slide 1 Periodic Table, Atomic Structure Physics 102: Lecture 25

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Page 1: Lect25 handout

Physics 102: Lecture 25, Slide 1

Periodic Table, Atomic Structure

Physics 102: Lecture 25

Page 2: Lect25 handout

Physics 102: Lecture 25, Slide 2

From last lecture – Bohr model

2 4 2 2

2 2 2

13.6 eV where / 2

2n

mk e Z ZE h

n n

2 2 2

2

10.0529 nm

2n

h n nr

mke Z Z

Ln = nh/2π

Angular momentum is quantized

Energy is quantized

Radius is quantized

n = 1, 2, 3 ...

Linear momentum too Bohr model is incorrect!

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Physics 102: Lecture 25, Slide 3

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

Note differences with Bohr model

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Physics 102: Lecture 25, Slide 4

ACT: Quantum numbers

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

1. n=1

2. n=2

3. n=3

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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:

n=1, l =0 is denoted as: 1s1

n=1 l =0 1 electron

Spectroscopic 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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Physics 102: Lecture 25, Slide 6

Electron orbitalsIn correct quantum mechanical description of atoms, positions of electrons not quantized, orbitals represent probabilities

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Physics 102: Lecture 25, Slide 7

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=2

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Physics 102: Lecture 25, Slide 8

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

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

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Physics 102: Lecture 25, Slide 9

Preflight 25.2

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

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Physics 102: Lecture 25, Slide 10

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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Physics 102: Lecture 25, Slide 11

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

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Physics 102: Lecture 25, Slide 12

s (l =0)

p (l =1)

d (l =2)

f (l =3)

n =

1,

2,

3,

...

The Periodic Table

What determines the sequence?Pauli exclusion & energies

Also s

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Physics 102: Lecture 25, Slide 13

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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Physics 102: Lecture 25, Slide 14

Sequence of shells:

4s electrons get closer to nucleus than 3d

Sequence of Shells

1s2s 2p3s 3p 3d4s 4p 4d 4f5s 5p 5d 5f6s 6p 6d ...

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

Pneumonic:

...

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Physics 102: Lecture 25, Slide 15

Properties of elementsWe can understand the different properties of elements from the periodic table

Noble gases• Filled outer p-shell (s for He)• Hard to ionize• Non-reactive

Alkali metals• Unpaired outer s-shell e–

• Easy to ionize• Very reactive

Transition metals• Filling d-shell (l = 2)• Tend to be magnetic

s2p6 s1

d1 – d10

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Physics 102: Lecture 25, Slide 16

Transition elements

Recall torque on current loop from B-field: = IABsin()

IA = -ep/(2rm) (r2) = -(e/2m)rp = -(e/2m)L

T = 2r/v = 2r/v = 2rm/p

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

High angular momentum

Strongly magnetic!

Use Bohr model: Ze

e–

This looks like a current loop!

I

I = -e/T A = r2

r

Angular momentum!

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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

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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.