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 exactlywhere electrons are - only know probabilities of where they could be
• Heisenberg Uncertainty Principle =
impossible to know both the velocity (or momentum) and position of an electron at the same time
Heisenberg Uncertainty Principle
Chapter 5
The Quantum Mechanical Model
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, 3p
y, 3p
z 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
• Will an electron fill the 1s or the 2s orbital first?
1s
2s2px 2py 2pzE
ne
rg
y
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
If we have 7 electrons, how will they fill in the below orbitals?
1s
2s2px 2py 2pzE
ne
rg
y
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.
• If we have 8 electrons, how will they be arranged?
1s
2s2px 2py 2pzE
ne
rg
y
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
Chapter 5
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
Energy Level
Sublevels 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
s
p
d
f
# of
shapes
Max
electrons
Starts at
energy level
Orbitals and Energy Levels
and so on....
1s
n = 1 2s
2p
n = 2 3s
3p
3d
n = 3
4s
4p
4d
4f
n = 4
Incre
asin
g e
nerg
y
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
2s
1s
3s
4s
2p
3p
4p
3d
Energ
y
Chapter 5
Electron Configuration
• Let’s determine the electron configuration for
Phosphorus
• Need to account for 15 electrons
Chapter 5
Incr
easi
ng e
ner
gy
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
3d
4d
5d
7p 6d
4f
5f
Chapter 5
• The first to electrons go into the
1s orbital
• Notice the opposite spins
• only 13 more
Incr
easi
ng e
ner
gy
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
3d
4d
5d
7p 6d
4f
5f
Chapter 5
• The next electrons go into the 2s
orbital
• only 11 more
Incr
easi
ng e
ner
gy
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
3d
4d
5d
7p 6d
4f
5f
Chapter 5
• The next electrons go
into the 2p orbital
• only 5 more
Incr
easi
ng e
ner
gy
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
3d
4d
5d
7p 6d
4f
5f
Chapter 5
• The next electrons go
into the 3s orbital
• only 3 more
Incr
easi
ng e
ner
gy
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
3d
4d
5d
7p 6d
4f
5f
Chapter 5
Incr
easi
ng e
ner
gy
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
3d
4d
5d
7p 6d
4f
5f
• The last three electrons
go into the 3p orbitals.
• They each go into
separate shapes
• 3 unpaired electrons
• 1s22s22p63s23p3
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
Chapter 5
Writing electron configurations
• Examples
• O 1s2
2s2
2p4
• Ti 1s2
2s2
2p6
3s2
3p6
3d2
4s2
• Br 1s2
2s2
2p6
3s2
3p6
3d10
4s2
4p5
• Core format
• O [He] 2s2
2p4
• Ti [Ar] 3d2
4s2
• Br [Ar] 3d10
4s2
4p5
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?
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