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11 Feb Start on the photoelectric effect, but decided to delay it until next time.
Thermal or black-body radiation. But first, what is a density -- precisely?
Precise definition of volume mass density. Then point out the other densities, such as population density. Then the density that defines the number of molecules per speed interval, dN/dv, for a gas. Finally, the one that I want is the energy per frequency interval for radiation inside an oven.
13 Feb Work out some details of the photoelectric effect. How do you measure the kinetic energy of the emitted electrons? Stop them with an applied voltage and see how much voltage it takes to do so. When you plot this stopping voltage versus the frequency of the incoming light the prediction of the theory is a straight line, and by measuring the slope of this line you have a value for the quotient h/e.
For thermal or black-body radiation, you can describe it most readily in terms of what happens inside an oven. The photons are bouncing around and within each volume DV of the space, there is an amount of energy, DE. You can further refine this by asking how much of this energy is in the frequency interval f to f + Df. This leads to the definition of an average energy density
then take the limit as DV and Df go to zero. This is denoted by u.
Planck figured out the structure of this function. First he did it experimentally, and found a formula that fit the data remarkably well. Then he discovered a mathematical derivation of the result, though one that depended on a remarkable and surprising assumption, that light is emitted and absorbed in discrete chunks.
15 Feb More on thermal radiation. What is the total energy density integrated over frequency? It's very easy to show that it is proportional to T4, though the factor requires doing a not-so-elementary integral.
That the peak of the distribution in occurs at a wavelength inversely proportional to the temperature is easy to show; it's a homework problem. It's application to the color of stars provides some direct and somewhat surprising inferences.
Compton scattering. What happens when a photon scatters from an electron? That this is a meaningful question necessarily comes after the idea that light comes in the form of photons. After that it is possible to write down the equations for conservation of energy and of momentum and to get a set of equations for some measurable quantities. After massaging the results, Compton found that the way to express the answer is in terms of wavelengths: