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Physics 102: Lecture 25
Periodic Table, Atomic Structure
Physics 102: Lecture 25, Slide 1
From last lecture – Bohr model
Angular momentum is quantized
Ln = nh/2π
n = 1, 2, 3 ...
Energy is quantized
mk 2e4 Z 2
13.6  Z 2
En  

eV  where  h / 2 
2
2
2
2
n
n
Radius is quantized
2
2
n2
 h  1 n
rn  
  0.0529 nm 

2
Z
 2  mke Z
Linear momentum too
Physics 102: Lecture 25, Slide 2
Bohr model is incorrect!
Quantum Numbers
Each electron in an atom is labeled by 4 #’s
n = Principal Quantum Number (1, 2, 3, …)
• Determines energy (Bohr)
l = Orbital Quantum Number (0, 1, 2, … n-1)
•
•
Determines angular momentum
l <n
always true!
L
h
(  1)
2
ml = Magnetic Quantum Number (-l , … 0, … l )
• Component of l
• | ml | <= l
always true!
ms = Spin Quantum Number (-½ , +½)
•
“Up Spin” or “Down Spin”
Physics 102: Lecture 25, Slide 3
h
Lz  m
2
Note differences
with Bohr model
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
Physics 102: Lecture 25, Slide 4
Spectroscopic Nomenclature
“Shells”
“Subshells”
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”
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”
1 electron in ground state of Hydrogen:
n=1, l =0 is denoted as: 1s1
n=1
Physics 102: Lecture 25, Slide 5
l =0
1 electron
Electron orbitals
In correct quantum mechanical description of atoms, positions of
electrons not quantized, orbitals represent probabilities
Physics 102: Lecture 25, Slide 6
Quantum Numbers
How many unique electron states exist with n=2?
l = 0 : 2s2
ml = 0 : ms = ½ , -½
2 states
l = 1 : 2p6
ml = +1: ms = ½ , -½
ml = 0: ms = ½ , -½
ml = -1: ms = ½ , -½
2 states
2 states
2 states
There are a total of 8 states with n=2
Physics 102: Lecture 25, Slide 7
ACT: Quantum Numbers
How many unique electron states exist with n=5
and ml = +3?
A) 0
B) 4
C) 8
D) 16
E) 50
Physics 102: Lecture 25, Slide 8
Preflight 25.2
What 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 9
Pauli Exclusion Principle
In an atom with many electrons only one electron
is allowed in each quantum state (n, l, ml, ms).
This explains the periodic table!
Physics 102: Lecture 25, Slide 10
Electron Configurations
Atom
Configuration
H
1s1
He
1s2
Li
1s22s1
Be
1s22s2
B
1s22s22p1
Ne
etc
1s22s22p6
s shells hold up to 2 electrons
Physics 102: Lecture 25, Slide 11
1s shell filled
(n=1 shell filled noble gas)
2s shell filled
2p shell filled
(n=2 shell filled noble gas)
p shells hold up to 6 electrons
The Periodic Table
s (l =0)
n = 1, 2, 3, ...
p (l =1)
Also s
d (l =2)
f (l =3)
What determines the sequence? Pauli exclusion & energies
Physics 102: Lecture 25, Slide 12
Shell Ordering
P(r)
Why do s shells fill first before p?
1s
P(r)
1s
2s
2p
r
2s electrons can get closer to nucleus, which
means less “shielding” from the 1s electrons
Physics 102: Lecture 25, Slide 13
r
Sequence of Shells
Pneumonic:
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d ...
Physics 102: Lecture 25, Slide 14
Sequence of shells:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, ...
4s electrons get closer to
nucleus than 3d
Properties of elements
We can understand the different properties of elements
from the periodic table
s2p6
s1
Noble gases
Alkali metals
• Filled outer p-shell (s for He)
• Hard to ionize
• Non-reactive
• Unpaired outer s-shell e–
• Easy to ionize
• Very reactive
d1 – d10
Transition metals
• Filling d-shell (l = 2)
• Tend to be magnetic
Physics 102: Lecture 25, Slide 15
Transition elements
In 3d shell we are putting electrons into l = 2; all atoms in
middle are strongly magnetic. Why?
r
Use Bohr model:
Ze
e–
This looks like a
current loop!
I
Recall torque on current loop from B-field: t = IABsin(f)
I = -e/T
T = 2r/v = 2r/v = 2rm/p
A = r2
IA = -ep/(2rm) (r2) = -(e/2m)rp = -(e/2m)L
High angular
momentum
Physics 102: Lecture 25, Slide 16
Strongly
magnetic!
Angular
momentum!
Sodium
Na
1s22s22p6 3s1
Single outer
electron
Neon - like core
Many spectral lines of Na are outer
electron making transitions
Yellow line of Na flame
test is 3p
3s
www.WebElements.com
Physics 102: Lecture 25, Slide 17
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 18