Lecture 4
Quantum Mechanics and Atomic Structure
I. The Quantization of Light and Atoms
A. Rutherford scattering and the "solar system" model of the atom;
to test the prevaling "plumb pudding" atomic model, Rutherford designed
a "scattering" experiment in which a
particles (positively charged subatomic particles = later determined to
be He nuclei) are bombarded against a very thin (several atomic layers
thick) metal foil
1. "plumb pudding" model: atoms consisted of a continuous
distribution of postive charge (the "pudding") with small negative particles
(electrons) imbedded in the positive charge; expected result - little deflection
of a particles
as they pass through the foil
2. actual result of experiment: a few a
particles were deflected almost 180 degrees; the new atomic model to explain
this result was called the "solar system" model in which the atom consisted
of a positive central nucleus containing most of the mass of the atom,
orbited by the negative electrons
3. one major inconsistancy with
the "solar system" model was that classical E&M theory predicted that
the orbiting (accelerating) electrons would continuously lose energy by
radiating electromagnetic waves and would quickly spiral into the nucleus
- the Bohr model (a modification of the Rutherford model) resolved the
problem by quantizing the electron orbits
B. Einstein and the photoelectric effect: while Einstein was
never completely confortable with quantum theory, he won a Nobel Prize
for his work explaining the photoelectric effect by treating light as "particles"
and became in effect one of the founding fathers of quantum theory
1. when light above a certain
"cutoff" frequency illuminated a metal electrode in a vacuum tube, electrons
were imediately ejected with a certain maximum kinetic energy depending
on the frequency of the light; classical E&M predicted that any frequency
light should be able to eject electrons given enough time for the electrons
in the metal to absorb enough energy from the light
2. in order to explain the behavior
of the photoelectric effect, Einstein imagined that the light could be
described as packets of energy (particle-like) called photons that interacted
with the electrons in the metal; each photon had an energy that was directly
proportional to the frequency of the light: Ephoton =
hf, where the proportionality constant h is Plank's constant
C. The Bohr model, line spectra
explained: in order to explain how atoms avoided quick destruction
by an electron "death-spiral", Bohr reasoned that the electrons could only
orbit in certain specific orbits and that the electrons did not interact
with light as a wave, but rather light as a particle (photon)
1. electrons in a Bohr atom may
move up or down into the discrete orbits only by absorbing or emitting
the exact amount of energy that is equal to the energy difference between
orbits, either by collisions with other atoms or by absorbing or emitting
a photon
2. the wavelengths of the line
spectra of the elements can be explained by the interaction of photons
with the atomic electrons; a continuous spectrum would consist of a continuous
distribution of photon energies, if these photon pass through a cool gas
of Bohr atoms only those photons of specific energy ( Ephoton =
energy difference between orbits) will be absorbed, this means certain
specific photon energys = specific frequencies or wavelengths would be
absorbed out of the spectrum = dark line or absorption line spectra; now
the electrons forced into the higher orbits or energy levels will spontaneously
decay back down to lower orbits or levels emitting a photon of specific
energy ( Ephoton = energy difference between orbits, again)
= specific frequencies or wavelengths would be emitted = bright line or
emission line spectra
II. The Wave-Particle Duality
of Nature
A. the particle-like nature of light - photons: the description of
light as a wave could NOT explain certain physical phenomena, so for certain
situations light must be described as a particle (photon)
B. the wave-like nature of particles - deBroglie waves: making
an analogy with Einstein's description of waves as particles, deBroglie
was able to describe particles (like the electron) as a wave; as an example
this could explain how the orbits of electrons were quantized, only those
orbits where the "electron wave" interfered constructively with itself
(a standing wave) were possible, at any other orbital radii the electron
wave would destructively interfer and cancel itself out and therefor the
electrons can only exist in certain orbits about the nucleus
C. these ideas led to one of the fundamental principles of quantum
theory: all matter and energy can only be described as a wave in
some situations and only as particles in other situations (but not both
at once); this is called the wave-particle duality of nature