Quantum Chemistry
{ Representing Electrons
Electrons as Waves?
As scientists discovered that light could
behave as both a wave and a particle,
Louis de Broglie wondered if electrons
could also have a dual wave-particle
nature as well.
De Broglie noticed similarities between
Bohr’s electron orbits and behaviour of
waves.
 He suggested that electrons could be
considered to be waves confined to the
space around the atomic nucleus.
 This would mean that electrons waves
could only exist at specific frequencies.
 By the formula E= hv, we know that
these frequencies are related to energy;
therefore, electron waves correspond to
the quantized energies of Bohr’s orbits.
Increasing energy
Fifth
Fourth  Further away from the
nucleus means more
Third
energy.
Second
 There is no“in
First
between” energy.
Nucleus  Energy Levels.
The Heisenberg Uncertainty
Principle
The idea of electrons having a dual waveparticle nature troubled scientists. If this is
so, where are electrons in the atom?
German physicist Heisenberg stated that it
is impossible to determine both the position
and velocity of an electron or any other
particle.
Quantum models predict the probability of
finding an electron.
The Quantum Mechanical
Model
 The atom is found
inside a blurry“electron
cloud”.
 A area where there is a
chance of finding an
electron.
Atomic Orbitals and Quantum
 Energy is quantized: It comes in chunks.
Numbers
 Quantum numbers specify the properties of
atomic orbitals and the properties of
electrons in orbitals.
 The main energy level, the shape, and
orientation of an orbital.
 Note: orbitals are not circular!
 Principle Quantum Number (n):
 Indicates the main energy level
 n =1, n = 2, n = 3, etc.
 Austrian physicist Schrodinger developed a
complex mathematical equation that
described the regions where there is a high
probability of finding an electron (shapes of
these regions or orbitals)
 Letters s, p, f, and d represent the shape of
the orbitals.
S Orbital
Starts in the first energy level
1 s orbital for energy
Spherical shaped
Each s orbital can hold 2 electrons
Called the 1s, 2s, 3s, etc.. orbitals.
P Orbitals




Start at the second energy level
3 different directions
3 different shapes
Each can hold 2 electrons
P Orbitals
D Orbitals
 Start at the third energy level
 5 different shapes
 Each can hold 2 electrons
F orbitals
 Start at the fourth energy level
 Have seven different shapes
 2 electrons per shape
Summary
# of
shapes
Max
electrons
Starts at
energy level
s
1
2
1
p
3
6
2
d
5
10
3
f
7
14
4
1st Energy level
Only s orbitals
Only 2 electrons
1s2
2nd Energy Level
Can have s and p orbitals
2 electrons in s and 6 electrons in p
2s22p6
Total electrons = 8
3rd Energy Level
Can have s, p, and d orbitals
2 electrons in s, 6 electrons in p, and 10
electrons in d
3s23p63d10
Total electrons = 18
4th Energy Level
Can have s, p, d, and f orbitals
2 electrons in s, 6 electrons in p, 10
electrons in d, and 14 electrons in f
4s24p64d104f14
Total electrons = 32
7p
7s
6s
6p
5p
6d
5f
5d
4f
4d
Increasing energy
5s
4p
3d
4s
3p
3s
2p
2s
1s
Electron Configurations
“Address for Electrons”
 Aufbau Principle:
 An electron occupies the lowest-energy
orbital that can receive it.
 Pauli Exclusion Principle:
 at most 2 electrons per orbital - different
spins
 Hund’s Rule:
 Orbitals of equal energy are each
occupied by one electron before any
orbital is occupied by a second electron.
Examples
What is the electron configuration for
phosphorus (P) ?
Phosphorus =15 electrons; these must be
accounted for in the orbitals.
Using our periodic table phosphorus = 3p
period; therefore, this will be the last orbital
in the electron configuration.
Fill orbitals from lowest to highest energy
level (ending at 3p)
 What is the electron configuration for calcium
(Ca)?
 What is the electron configuration for fluorine
(F)?
Exceptions to Electron
Configuration
 Write the electron
configuration for titanium.
 1s22s22p63s23p64s23d2
yes
 Write the electron configuration for
vanadium.
yes
 1s22s22p63s23p64s23d3
 Write the electron configuration for
chromium.
 1s22s22p63s23p64s23d4 no
 These numbers are expected, but
wrong!
Chromium
 Actually is…
 1s22s22p63s23p64s13d5
 Why?
 This gives us two half filled orbitals.
 Slightly lower in energy.
 Makes them more stable.
 Changes the filling order.
 The same principal applies to copper,
gold, silver, molybdenum, and tungsten
Copper
 Write the electron configuration for copper.
 Copper has 29 electrons
 Copper is in the 3d period; therefore, the
electron configuration must end in 3d
 1s2 2s2 2p6 3s2 3p6 4s2 3d9
 But this is incorrect!
 Actually… 1s2 2s2 2p6 3s2 3p6 4s1 3d10