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

2. From last lecture – Bohr model
Angular momentum is quantized
Ln = nh/2π
n = 1, 2, 3 ...
Energy is quantized
Radius is quantized
Momentum too

3. Quantum Numbers l = Orbital Quantum Number (0, 1, 2, … n-1)
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!
ml = Magnetic Quantum Number (-l , … 0, … l )
Component of l
| ml | <= l always true!
Start by asking students to name seat (use row and number) make analogy with Quantum numbers.
ms = Spin Quantum Number (-½ , +½)
“Up Spin” or “Down Spin” 10

4. ACT
For which state of hydrogen is the orbital angular momentum required to be zero?
75%
15%
10%
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. 12

5. Nomenclature Example l =0 is “s state” l =1 is “p state”
“Shells”
“Subshells”
l =0 is “s state”
n=1 is “K shell”
l =1 is “p state”
n=2 is “L shell”
l =2 is “d state”
n=3 is “M shell”
l =3 is “f state”
n=4 is “N shell”
l =4 is “g state”
n=5 is “O shell”
Example
1 electron in ground state of Hydrogen:
n=1, l =0 is denoted as: 1s1
n=1
l =0
1 electron 14

7. Quantum Numbers Example There are a total of 8 states with n=2 l = 0 :
How many unique electron states exist with n=2?
l = 0 :
ml = 0 : ms = ½ , -½ 2 states
2s2
l = 1 :
ml = +1: ms = ½ , -½ 2 states
ml = 0: ms = ½ , -½ 2 states
ml = -1: ms = ½ , -½ 2 states
2p6
There are a total of 8 states with n=2 16

8. ACT: Quantum Numbers There are a total of 4 states with n=5, ml = +3
How many unique electron states exist with n=5 and ml = +3?
A) B) C) D) E) 50
Only
l = 3 and l = 4
have ml = +3
l = 0 : ml = 0
l = 1 : ml = -1, 0, +1
l = 2 : ml = -2, -1, 0, +1, +2
l = 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 20

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?
ml = -4 : ms = ½ , -½ 2 states
18 states
2*9
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
in general,
2*(2l+1)
ml = +3: ms = ½ , -½ 2 states
ml = +4: ms = ½ , -½ 2 states 27

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!
Note it isn’t electron charge that keeps them from being in the same state! 25

11. Electron Configurations
Atom Configuration
H 1s1
He 1s2
1s shell filled
(n=1 shell filled - noble gas)
Li 1s22s1
Be 1s22s2
2s shell filled
B 1s22s22p1
etc
(n=2 shell filled - noble gas)
Ne 1s22s22p6
2p shell filled
p shells hold up to 6 electrons
s shells hold up to 2 electrons 29

13. Shell Ordering P(r) Why do s shells fill first before p? r 2s P(r) 1s
Show models
2s electrons can get closer to nucleus, which means less “shielding” from the 1s electrons r 31

14. Sequence of Shells Sequence of shells: 1s,2s,2p,3s,3p,4s,3d,4p…..
4s electrons get closer to nucleus than 3d 1s 2p 3p 4p 5p
4p(Kr)
5s(Rb),4d,5p(Xe)
6s(Cs),4f(Ce),5d(La),6p(Rn) 4f 5f 33

15. Sequence of Shells 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 33

16. Sodium Example Single outer electron Na 1s22s22p6 3s1 Neon - like core
Many spectral lines of Na are outer electron making transitions
Yellow line of Na flame test is 3p s 35

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. 40