Periodic Table
Quantum Numbers
 The Bohr model of hydrogen
provided a single quantum
number n.
• Principal quantum number
• One-dimensional solution
 Schrödinger’s equation for a
real atom is 3-D.
• Two other quantum
numbers
• Orbital angular momentum
• Orbital magnetic number
1
2
3
Shells for the principal
quantum number n
Orbital Shells
 The orbital angular
momentum l is quantized in
steps of h.
• Values from 0 to n-1
 The values are named
based on early
spectroscopy.
• n shells 1=K, 2=L, 3=M,
4=N, 5=O
• l shells 0=s, 1=p, 2=d, 3=f,
4=g
A. Clark, Chemical Computing Group
Zeeman Effect
Lz  ml 
 Spectral lines from atoms in a
strong magnetic field are split.
• Zeeman effect
• Magnetic moment of orbiting
electron
 Orbital magnetic number ml
lines up with applied field.
• Values from –l to l
• Lz is with respect to field
Spin
 Electrons possess intrinsic
angular momentum.
• Spin angular momentum s
• Spin magnetic number ms
 No two atomic electrons can
occupy the same set of
quantum numbers.
• Pauli exclusion principle
• Applies to fermions
 Electron spin s can only have
one value: 1/2.
• ms = +1/2 or -1/2
• Spin up or spin down
 Photons are spin 1
Electron Configurations
 Electrons in atoms populate
the lowest energies first.
• Two electrons per state for
spin
 Atoms have unique ground
states.
•
•
•
•
Hydrogen has 1 1s electron
Helium adds another 1s
Lithium must start 2s shell
Boron starts 2p shell which
holds 6 electrons
H
1s
He 1s 2
Li
1s 2 2 s
Be
1s 2 2s 2
B
1s 2 2s 2 2 p
C
1s 2 2s 2 2 p 2
N
1s 2 2s 2 2 p 3
O
1s 2 2s 2 2 p 4
Germanium
 Germanium (Ge) has an
atomic number of 32. Find the
shell configuration for the
ground state.
 Start counting shells from the
lowest state.
•
•
•
•
•
•
•
•
n = 1, l = 0: 1s – 2 electrons
n = 2, l = 0: 2s – 2 electrons
n = 2, l = 1: 2p – 6 electrons
n = 3, l = 0: 3s – 2 electrons
n = 3, l = 1: 3p – 6 electrons
n = 3, l = 2: 3d – 10 electrons
n = 4, l = 0: 4s – 2 electrons
n = 4, l = 1: 4p – 2 electrons
 Total 2+2+6+2+6+10+2+2=32
1s 2 2s 2 2 p 6 3s 2 3 p 6 3d 10 4s 2 4 p 2
Organized Table
 The periodic table was organized to explain chemical
properties.
• Quantum physics explained structure
Energy Levels
 Subshell: S G F D P
 Period
• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
 The shells don’t fill up in exact
order.
1s
2s
3s
4s
5s
6s
7s
8s
3d
4d
4f 5d
5f 6d
5g 6f 7d
2p
3p
4p
5p
6p
7p
8p
 Energy levels are determined
by quantum calculations.
• General patterns exist
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