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Chapter 5
Quantum Theory and Electron Configurations
Quantum-Mechanical Model of the
Atom
• Since the Bohr model had a very limited
use, a new and very different model of
the atom exists
• The Quantum Mechanical Model
(1926) contains:
 Quantum energy levels
 Dual wave/particle nature of electrons
 Electron clouds
• In the new model, don’t know exactly
where electrons are - only know
probabilities of where they could be
Heisenberg Uncertainty Principle
• Heisenberg Uncertainty Principle =
impossible to know both the velocity (or
momentum) and position of an electron at the
same time
The Quantum Mechanical Model
Chapter 5
Quantum Mechanical Model
• Einstein (1905)
 Light consists of quanta, called
photons
 Photoelectric Effect – Sunlight
striking a sheet of metal will
knock off the outermost electrons
and move, causing an electric
current
• de Broglie (1924) = Photons
both particles and waves
• Davisson (1927) = Electrons
both particles and waves
Quantum-Mechanical Model of the
Atom
• Orbital = region around nucleus where an
electron with a given energy level will
probably (90%) be found
• Four kinds of orbitals
s - spherical in shape, lowest orbital for every
energy level
p - dumbbell shaped, second orbital
d - complex “flower” shape, third orbital
f - very complex shape, highest orbital
s-orbitals
• All s-orbitals are spherical.
• As n increases, the s-orbitals get larger.
p- orbitals
• Three p-orbitals: px, py, and pz
 Lie along the x-, y- and z- axes of a Cartesian
system.
 Dumbbell shaped, gets larger as n increases
d and f - orbitals
• There are five d and seven
f-orbitals.
Quantum Mechanical Model
• Principle Energy Levels (n)
 Labeled from 1-7
 First energy level is n=1
 Contains sublevels (s, p, d and f)
• Each energy level contains the number of sublevels equal to it’s value
for n
– If n=3, there are three sublevels
Quantum Mechanical Model
• In each sublevel there are atomic orbitals
• Atomic orbitals – describe a space where an electron is
likely to be found
Type of
subshell
Shape of
orbitals
Number of
orbitals
Orbital
‘names’
s
Spherical
1
s
p
Dumbbell
3
px, py, pz
d
Cloverleaf
(and one
donut)
5
f
Multi-lobed
7
Quantum Mechanical Model
• Each orbital can contain two electrons.
• Since negative-negative repel, these electrons occupy
the orbital with opposite spins.
Quantum Mechanical Model
• The total number of orbitals of an energy level is n2.
 For the third principle energy level, n=3, which means there are
9 orbitals
• These orbitals are 3s, 3px, 3py, 3pz and the 5 d orbitals
• Remember, we no longer think of orbitals as concentric
circles, but we can say that n=4 extends farther from the
nucleus than n=1.
Valence Electrons
• Only those electrons in the highest principle energy
level
Electron Configuration and Orbital Notation
• Aufbau Principle – electrons fill lower energy orbitals first,
“bottom-up”
 n=1 fills before n=3
Energ
y
• Will an electron fill the 1s or the 2s orbital first?
2s
1s
2px
2py
2pz
Electron Configuration &Orbital Notation
• Hund’s Rule – electrons enter same energy orbitals so that
each orbital has one electron before doubling up
 Each of the first electrons to enter the equal energy orbitals must
have the same spin
Energ
y
 If we have 7 electrons, how will they fill in the below orbitals?
2s
1s
2px
2py
2pz
Electron Configuration and Orbital Notation
• Pauli Exclusion Principle – an orbital can contain no more
than 2 electrons. Electrons in the same orbital must have
different spins.
Energ
y
• If we have 8 electrons, how will they be arranged?
2s
1s
2px
2py
2pz
Apartment Analogy
•
•
•
•
Atom is the building
Floors are energy levels
Rooms are orbitals
Only two people per room
Orbital Diagrams
• Draw each orbital as a box.
• Each electron is represented using an arrow.
 Up arrows – clockwise spin
 Down arrows – counter-clockwise spin
• Determine the total number of electrons involved.
• Start with the lowest energy level (1s) and start filling in
the boxes according the rules we just learned.
Transition Metal Exceptions
• Can move from the highest filled s orbital to create a fully
filled, or half filled d or f
• TRANSITION METAL EXCEPTIONS
Total # of electrons in an Energy Level
• 2n2
• n=1
2 x 12 + = 2
• n=2
2 x 22 + = 8
• n=3
2 x 32 + = 18
•
•
•
•
n=4
n=5
n=6
n=7
Chapter 5
Orbitals and Energy Levels
Principal
Sublevels
Energy Level
Orbitals
n=1
1s
1s (one)
n=2
2s , 2p
2s (one) + 2p (three)
n=3
3s , 3p , 3d
3s (one) + 3p (three) + 3d (five)
n=4
4s, 4p, 4d, 4f
4s (one) + 4p (three) + 4d (five)
+ 4f (seven)
Chapter 5
Summary
# of
Max
shapes electrons
s
p
d
f
Chapter 5
Starts at
energy level
Orbitals and Energy Levels
n=4
Increasing energy
n=3
n=2
n=1
1s
2p
2s
3d
3p
3s
4f
4d
4p
4s
and so on....
Orbital Diagrams
• Orbital diagrams are used
to show placement of
electrons in orbitals.
• Need to follow three
rules (Aufbau, Pauli,
Hund’s) to complete
diagrams
Li
Be
B
C
N
Ne
Na
Orbital Diagram
4p
3d
Energy
4s
3p
3s
2p
2s
1s
Electron Configuration
• Let’s determine the electron configuration for
Phosphorus
• Need to account for 15 electrons
Chapter 5
Increasing energy
7s
6s
5s
7p
6p
6d
5d
5p
4d
4p
3d
4s
3p
3s
2p
2s
1s
Chapter 5
5f
4f
Increasing energy
7s
6s
5s
7p
6p
6d
5d
5p
4d
4p
3d
4s
3p
3s
2p
2s
5f
• The first to electrons go into the
1s orbital
• Notice the opposite spins
• only 13 more
1s
Chapter 5
4f
Increasing energy
7s
6s
5s
7p
6p
6d
5d
5p
4d
4p
3s
2p
4f
3d
4s
3p
5f
• The next electrons go into the 2s
orbital
• only 11 more
2s
1s
Chapter 5
Increasing energy
7s
6s
5s
7p
6p
6d
5d
5p
4d
4p
3d
4s
3s
2s
3p • The next electrons go
into the 2p orbital
2p
• only 5 more
1s
Chapter 5
5f
4f
Increasing energy
7s
6s
5s
7p
6p
6d
5d
5p
4d
4p
3d
4s
3s
2s
3p • The next electrons go
into the 3s orbital
2p
• only 3 more
1s
Chapter 5
5f
4f
Increasing energy
7s
6s
5s
4s
7p
6p
6d
5d
5p
4d
4p
3p •
3s
2s
1s
2p •
•
•
5f
4f
3d
The last three electrons
go into the 3p orbitals.
They each go into
separate shapes
3 unpaired electrons
1s22s22p63s23p3
Chapter 5
Writing Electron Configuration
• Determine the total number of electrons.
• Write the principle energy level number as a coefficient,
the letter for the subshell, and an exponent to represent
the number of electrons in the subshell.
• He: 1s2
The Kernel (Noble Gas) Notation
• Determine the total number of electrons
• Find the previous noble gas and put its symbol in brackets
• Write the configuration from that noble gas forward as
usual
Writing electron configurations
• Examples
•
•
•
O
Ti
Br
•
Core format
•
•
•
O
Ti
Br
1s2 2s2 2p4
1s2 2s2 2p6 3s2 3p6 3d2 4s2
1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p5
[He]
[Ar]
[Ar]
2 s 2 2 p4
3d2 4 s 2
3d10 4s2 4p5
Chapter 5
Quantum Numbers
• Each electron can be described by four numbers unique to that
electron (like a fingerprint)
• “n” – the principal quantum # describes the principal energy
level, n=1, 2, 3…,7
• “l” – describes the shape of subshell
 s subshell = 0
 p subshell = 1
 d subshell = 2
 f subshell = 3
• “m” –describes the orientation , m = -l….0….+l
• “s” – describes the spin, s=1/2 or -1/2
Quantum Numbers
• Example: Look at carbon’s orbital diagram which contains 6
electrons. What are the quantum #s for the last electron to be
filled?
• Example: Look at Vanadium’s Kernel notation. Do the
orbital diagram for only the valence electrons. What are the
quantum #’s for the second to last electron to be filled?