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Physics 102: Lecture 25, Slide 1
Physics 102: Lecture 25
Periodic Table, Atomic Structure
Physics 102: Lecture 25, Slide 2
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 3
Bohr model is incorrect!
Quantum Mechanics (vs. Bohr)
• Predicts available energy states agreeing with Bohr.
En same as Bohr model
• Don’t have definite electron position, only a
probability function. Bohr: definite e- position rn
• Each orbital can have 0 angular momentum!
Bohr: Ln = nh/2, n = 1,2,3 ...
• 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) Bohr: one number n
ms = spin (-½ , +½)
Physics 102: Lecture 25, Slide 4
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 5
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 6
The allowed values of l are
0, 1, 2, …, n-1. When n=1, l
must be zero.
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 7
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 8
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 9
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
l
l
l
l
= 0 : ml = 0
= 1 : ml = -1, 0, +1
= 2 : ml = -2, -1, 0, +1, +2
Only
l = 3 and l = 4
have ml = +3
= 3 : ml = -3, -2, -1, 0, +1, +2, +3
ms = ½ , -½
2 states
l = 4 : ml = -4, -3, -2, -1, 0, +1, +2, +3, +4
ms = ½ , -½
2 states
There are a total of 4 states with n=5, ml = +3
Physics 102: Lecture 25, Slide 10
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 :
ml = -3 :
ml = -2 :
ml = -1 :
ml = 0 :
ms = ½ , -½
ms = ½ , -½
ms = ½ , -½
ms = ½ , -½
ms = ½ , -½
2 states
2 states
2 states
2 states
2 states
ml = +1: ms = ½ , -½
ml = +2: ms = ½ , -½
2 states
2 states
ml = +3: ms = ½ , -½
ml = +4: ms = ½ , -½
2 states
2 states
Physics 102: Lecture 25, Slide 11
18 states
2*9
in general,
2*(2l +1)
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 12
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 13
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 14
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 15
r
Sequence of Shells
Pneumonic:
1s
2s 2p
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d ...
YOU DO
THE REST!
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
1s
2s
3s
4s
3d
2p
3p
4p
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 17
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rm/p
A = r2
IA = -ep/(2rm) (r2) = -(e/2m)rp = -(e/2m)L
High angular
momentum
Physics 102: Lecture 25, Slide 18
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 19
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 20