Unit 1 – Structure and
Properties
3.7 – Wave Mechanics and
Orbitals
Quantum Mechanics
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Three main scientists revolutionized this
field – de Broglie, Schrödinger, and
Heisenberg
It began not long after the introduction
of the Bohr atom
There was a lot of heated debate over
who was correct
de Broglie (de broy)
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Young French physicist, was the first to turn
around the idea of wave-particle duality
 If waves can exhibit particle-like behavour,
particles can exhibit wave-like behaviour
Thanks to fancy math, it is possible to
calculate the wavelength of matter based on
its mass and speed
(And also the mass of a photon based on its
wavelength and frequency)
What?
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If you were to run the numbers, a 100
g golf ball traveling at 35 m/s has a
wavelength of 1.9 x 10-34 m
That is VERY SMALL, and so the effect
of this are never perceived, and we
think of a golf ball as a particle only
Electrons
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The mass of an electron is very small
compared to that golf ball, and so when
similar calculations are performed, the
wavelength of the electron is large
enough to contribute to its overall
characteristics
If an electron is a wave, it can be
described by some very fancy math
called a wave function
Waves?
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The concept of electrons as standing
waves around the nucleus can fit all of
the previously observed characteristics
(discrete energy levels, transitions from
level to level, no loss of energy)
Wave have wavelengths, and standing
waves can only have whole number
multiples of wavelengths
Show the simulation!
Schrödinger
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Did fancy math describing electrons as
wave functions
Called wave mechanics – because of
the contributing ideas – called quantum
mechanics.
Hard to visualize how math can be
matter
Heisenberg
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If an electron is not orbiting in a circle,
but rather it is a wave, how is an
electron moving? Where exactly is it?
We don’t know
This reasoning comes from the work of
Heisenberg, called the Uncertainty
Principle
Uncertainty Principle
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To observe an electron, we would have
to shine energy on it in some way.
Shining energy on it will change its
position and speed
According to this principle, it is
impossible to simultaneously know the
exact position and speed of a particle
Uncertain?
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The math behind the uncertainty principle
takes into account the mass of the object in
question
For massive object, say me, the uncertainty
principle doesn’t apply
For the electron however, it certainly does
It is therefore not appropriate to assume
that the electron is moving around the
nucleus in a well defined circle or shell
Visualization
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There is a very helpful way to apply
Heisenberg’s and Schrödinger’s math to
help us visualize the atom.
The math describes information and
position and the probability of location,
and we can therefore convert the wave
functions into a 3D electron density
probability map called an ORBITAL
Orbitals
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Each orbital can contain two electrons
We can now think of each electron shell
surrounding an atom as made up of subshells, which are in turn made up of
orbitals
The orbitals have names, and specific 3D
shapes that represent the space where
there is a 90% chance of finding the
electron
s subshell
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The first subshell is the s subshell
containing 1 s orbital
It is spherical in shape
It is the lowest energy orbital of the
shell
Two electrons fit here
NOTE – the first electron shell only
holds 2 electrons – only has 1 subshell
p subshells
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The p subshells is made up of 3 p orbitals
Each p orbital is dumbbell shaped, or has
two lobes on either side of the nucleus, and
are oriented differently in space, px, py, and
pz
The p sub-shell can hold a total of 6
electrons
In the 2nd shell there is one 2s orbital and 3
2p orbitals, for a total of eight electrons
d subshell
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The d orbitals have interesting shapes
There are 5 d orbitals in the d subshell
The d subshell can hold a total of 10
electrons
So.
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How do these bubbly diagrams relate to
what we already know?
Each orbital can accommodate two electrons
Each shell can hold more electrons, and is
farther away from the nucleus
Valence electrons confer chemical properties
The shape of the periodic table shows the
way…..
s orbitals are filled here
p orbitals are filled here
d orbitals are filled here
f orbitals are filled here
s
p
d
f
The orbital order can be determined by counting
up the periodic table using the atomic number.
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
3d
4d
5d
4f
5f
The order in which orbitals are filled with
electrons can be determined by counting up the
periodic table using the atomic number.
3d x2 - y2 2py
3dyz
1s
+
3dxz
2px
2s
3dxy
3s
3pz
3d z2
3py
4s
3px