Download Periodic Table, Atomic Structure

Physics 102: Lecture 25
Periodic Table, Atomic Structure
• Today’s Lecture will cover Section 28.7
Make sure your grade book entries are correct.
Physics 102: Lecture 25, Slide 1
Quantum Numbers
Each electron in an atom is labeled by 4 #’s
n = Principal Quantum Number (1, 2, 3, …)
• Determines energy
ℓ = Orbital Quantum Number (0, 1, 2, … n-1)
•
•
Determines angular momentum L 
h
(  1)
2
mℓ = Magnetic Quantum Number (ℓ , … 0, … -ℓ )
• Component of ℓ
•
ms = Spin Quantum Number (+½ , -½)
•
“Up Spin” or “Down Spin”
h
Lz  m
2
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 3
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 4
Nomenclature
“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”
“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”
1 electron in ground state of Hydrogen:
Physics 102: Lecture 25, Slide 5
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 6
ℓ =0
1 electron
Quantum Numbers
How many unique electron states exist with n=2?
Physics 102: Lecture 25, Slide 7
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 8
ACT: Quantum Numbers
How many unique electron states exist with n=5
and ml = +3?
Physics 102: Lecture 25, Slide 9
ACT: Quantum Numbers
How many unique electron states exist with n=5
and mℓ = +3?
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
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 11
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 12
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 13
18 states
Electron Configurations
Atom
Configuration
H
1s1
He
1s2
Li
1s22s1
Be
1s22s2
B
1s22s22p1
etc
Ne
1s22s22p6
s shells hold up to 2 electrons
Physics 102: Lecture 25, Slide 14
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
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
Sequence of shells:
1s,2s,2p,3s,3p,4s,3d,4p…..
4s electrons get closer to
nucleus than 3d
19 20 21 22 23 24 25 26 27 28 29 30
K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn
4s
4p
3d
In 3d shell we are putting electrons into ℓ = 2; all
atoms in middle are strongly magnetic.
Angular
momentum
Physics 102: Lecture 25, Slide 16
Loop of
current
Large magnetic
moment
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
ICES Forms – Don’t Leave Yet!
• Read Textbook Section 27.4
See you later!
Physics 102: Lecture 25, Slide 19