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