In this module, we will be looking at waves, but the only ones of interest to us
are electromagnetic waves travelling at the speed of light, c.  For these, the
equation c = λv establishes that the wavelength, λ, and the
frequency, v, are inversely proportional. In 1900, physicists were aware of a
few phenomena that classical physics simply could not explain.  To treat these,
scientists introduced fixes that went against classical physics, but managed to
explain the otherwise unexplainable.  Planck hypothesized that energy comes in
discrete bundles called quanta whose individual energies, E, are directly
related to frequency by E = nhv, where h is Planck’s constant and n is a
positive whole number. Soon after, Einstein proposed that light
not only behaved as a wave it also
behaved as a particle these particles of
light, or photons, had an energy hγ where h is again Planck’s constant.
Finally, Bohr explained the spectrum of the hydrogen atom by proposing that
electrons can only occupy specific orbits defined, like Planck, by positive
whole numbers. A fundamentally new approach to physics, called quantum
physics, came with the subsequent contributions of de Broglie, Heisenberg, and
Schrodinger.  It is necessary to explain the physics of very small systems.
Chemistry deals with atoms and molecules, and their incredibly small size thus
insists upon the use of quantum physics.  Inspired by Einstein’s wave/particle
duality of light, de Broglie proposed wave/particle duality for matter.  Matter’s wave
nature was a radical proposal, and a seemingly needless one as nobody had
ever really noted it in any way.  However, he proposed that a particle had a
wavelength, λ, given by h / m v, where h is, yet again, Planck’s constant, and m
and v are the mass and velocity of the particle.  For macroscopic objects, its
wavelength is simply too small to be
observed however for an electron its
wavelength is small, but larger than the size of the atom it occupies.  In other
words, if we ignore the particle/wave duality of the electron,
we cannot accurately describe the behaviour of atoms and molecules.
Building upon matter’s particle/wave duality,
Heisenberg proposed the uncertainty principle stating that it is impossible
to know, with infinite precision, both the position and momentum of a particle.  Note
that this is not a comment on the precision of our instruments.
It is a fundamental law of nature.  For macroscopic particles, the uncertainties
involved are incredibly small.  However, like de Broglie, when applied to
very small systems, they cannot be ignored.
Our physical description of atoms and molecules would be totally incorrect as
the uncertainties in the electrons’ positons are actually larger than the
dimensions of these atoms and molecules.  It would be like saying the
inhabitant of a house is positioned somewhere in, or close to, the house he is
currently occupying:  a rather pointless statement.  To handle small systems,
Schrödinger gave us his equation, HΨ = EΨ, where H is the Hamiltonian
operator, E is the numerical value of the system’s energy, and Ψ is the wavefunction
The Hamiltonian operator is a representation of all of the energy terms,
both kinetic and potential, that respects Heisenberg’s principle that position and
momentum and thus potential energy and
kinetic energy cannot be both known with
infinite precision.  Its precise nature is beyond the scope of this course.  The wavefunction
squared tells us everything we can know about the position of the
electrons, and this limits us to probabilities.  Heisenberg precludes
certainty:  we can only talk in terms of probability.
