"I think it is safe to say that no one
understands quantum mechanics."
Physicist Richard P. Feynman
The nature of the nucleus was determined
using radiation (Rutherford’s gold foil
The quantum nature of electrons was
demonstrated by Bohr using spectroscopy.
Using quantum numbers, electrons are
defined as occupying orbitals within
successively larger shells.
Each orbital can contain 2 electrons of
What do electron orbitals look like?
Although math could be used to
describe the energy of electrons, what
they are doing, or what they really are
was still very unclear.
Are electrons particles? Waves?
Both? Something else?
Louis de Broglie (1892-1987)
Louis de Broglie (1892-1987) was a
In 1922, he hypothesized that not only
electrons, but ALL matter exhibits
both particle AND wave-like
However, the larger the particle, the
smaller the wave-like properties
The de Broglie hypothesis stated that:
Any moving particle or object has an
This united Einstein’s work on light
and matter, and created a new branch
of physics, called wave mechanics.
Electron can be thought of as
standing waves. (think skipping
Erwin Schrödinger (1887 – 1961)
In 1926, Erwin Schrödinger discovered
a set of equations that described the
structure of orbitals.
His math was based on Louis de
Broglie’s concept of electrons as
This was the one of the earliest
formulations of Quantum mechanics.
Schrödinger’s equations defined the
most probable position of an electron
in an atom.
An orbital is defined as the area within
which the electron will most likely be
Orbitals are not uniform; within all
orbitals, there are different probabilities
of where the electron will be.
The hydrogen atom has one
electron in a 1s orbital. As the
distance from the nucleus 0.05 0.15
increases, the probability of the
electron occurring at that point nucleus in nm
first increases, then diminishes to
the point of virtual nothingness
must think in
finding the 0.05 0.15
electron is the
same no nucleus in nm
Electron orbitals can be thought of as
an electron cloud.
This cloud is a probability map of where
electrons are most likely to be found
around the nucleus.
The opacity of the cloud is proportional
to the probability density.
Orbitals can thus be viewed as a 3D
electron probability density map that
outlines the area the electron is
The shape of an orbital is determined
by the 2o quantum number, l.
The orientation is determined by the
magnetic number, ml.
1s (l = 0, ml = 0)
2s (l = 0, ml = 0)
2p (l = 1, ml = 0)
2p (l = 1, ml = -1)
2p (l = 1, ml = +1)
Simultaneously, Werner Heisenberg
also developed a set of equations that
explained the behaviour of electrons.
This was called matrix mechanics.
However, the math was so
complicated, that Heisenberg himself
did not fully understand why it
explained the quantum nature of
Heisenberg and Schrödinger’s
discoveries gave birth to quantum
Quantum mechanics explains (and
makes predictions!) about the natural
laws that govern at the molecular
One of the consequences of quantum
mechanics is that it is not possible to
simultaneously know the position and
momentum (speed and direction) of a
This was determined by Heisenberg,
and is hence called the Heisenberg
Essentially, the Uncertainty Principle exists
because to determine the property of a
particle, one must interact with it.
This interaction with the particle will alter the
properties of the particle.
At the atomic level, the interactions between
particles becomes very significant.
Thus, the smaller the system to be
observed, the greater the effect of the
#12-19 (multiple choice)
#4-6, 9-17 (short answer)