First step toward the Quantum, Light in a Box. Take a box, in thermal equilibrium at a certain temperature, hot enough so that we can observe the light coming out of a little hole. Think oven.
Thermal equilibrium has quite a long history: thermodynamics and statistical theory of gases etc. Hard to escape that each degree of freedom must have the same average energy.
We said “very blue” = violet comes after blue in the spectrum, so the prediction that the spectrum is crowded toward the short wavelengths was called the “ultraviolet catastrophe”
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Planck thought this was a weird condition. It was soon seen (by Einstein) that this explains lots of other things too. The specific heat of a gas of hydrogen molecules, H2 is rather strange (= amount of energy to increase temperature by one degree)
Photoelectric effect: “photons” are real!---Einstein’s first home-run. (“Photon” is a term to describe the quantum of light.) The experiment, in a vacuum illuminated by a selected wavelength of light illuminating a clean metal surface:
What would we expect? We are kicking electrons out of the metal. They didn’t just fall out, so they must be bound. Model binding by a spring, which we have to break to get the electron out. The electric field of the light wiggles the electron, pumping in energy until we break the spring. Expect:
What is seen:
Typical experiment results
The Einstein theory
Quick revisit of how we know that light is a wave (after all, Newton had decided that light was particles moving with c): Thomas Young (1801) was skillful enough to see interference from two slits:
Compton said, let’s use a wave-type device to choose light (waves) of a given wave length and then scatter them from an electron, a billiard ball-type experiment, and then make another wave-type measurement to see if we can predict their new wavelength, if they still have one:
For the electron, the lightest particle around to scatter from,
For just now, we can summarize the wave-particle puzzle by saying that when we do a wave-type experiment, light behaves like a wave. When we do a particle-type experiment, light behaves like a particle. When the two are combined, as in the Compton scattering experiment, the behavior of the light switches back and forth according to the demands made on it by the actual apparatus used. The key new point here is the fact that the measuring apparatus seems to affect the physical system, instead of just recording some pure reality.
A look at atoms, with the quantum in mind.
Breakthrough! Rutherford calculated the small deflection an alpha particle (Helium nucleus from a radioactive element) passing through a very thin foil of a heavy element (gold)
In Rutherford’s words “It was as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”
Bohr saw that the quantum concept could be the answer, and he knew too, that he didn’t know enough to make a true model, so he tried something provisional, rather a new style. His propositions:
The calculation is simple:
The energy of the atom is the sum of the kinetic energy and the potential energy:
Email: willis@nevis1.columbia.edu
Home Page: www.nevis.columbia.edu/~willis
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