Issued Wed, Jan 24 Due Wed, Jan 31

Required reading: F+T 1.4 , 1.7 (Opt: Beiser 9.5-9.7, 4.1, 4.2, 4.Appendix)

1a) F+T 1.12. BUT do not use the value . INSTEAD, use the value . (This is roughly the potential in t.v. tubes) The last part of the question is the same, "How much is the result modified if the metal's 4-eV work fn is taken into account?" (Be explicit - which WAY is it modified?)

1b) F+T 1.5

2a) What is the energy and momentum of an x-ray photon whose wavelength is 12.0 pm (= 12.0 picometers = m)?

b) If these 12.0 pm photons are scattered from a target by the Compton effect, what wavelength and momentum will the outgoing x-ray photons have if they are observed 90 degrees from the incident beam?

c) If the target is made of copper (atomic weight of Cu=63 amu, 1 amu = 932 MeV/c^2), what is the Compton wavelength ( h/mc) of Cu atoms?

d) If our 12.0 pm photons scatter from Cu atoms (not electrons), what wavelength will the outgoing photons have if they are observed 90 degrees from the incident beam? How does this compare with parts a) and b)?

3a) In question 2b (12 pm photons, scattering 90 degrees off of electrons) what is the energy, and the magnitude of the momentum of the recoiling electrons? (Hint: Recall, for relativistic particles)

3b) Show that it is impossible for a photon to give up all its energy and momentum to a free electron. (In other words: you cannot have a photon come in, hit a lonely still-standing electron, and get absorbed turning all its energy into kinetic energy of the electron. This is the reason why the photoelectric effect can take place only when photons strike bound electrons!) Hint: For a photon, E=pc (E is the energy and p is the momentum) For electrons, . Use conservation of energy and momentum.

4a) We talked in class about Planck's radiation formula for blackbodies, namely , where u is the energy density as a function of the frequency, , of the emitted light. (k is Boltzman's constant=8.6*10^-5 eV/K, T the temperature in Kelvins, and h is Planck's constant.) For long wavelengths, show that your formula reduces to the Rayleigh-Jeans law, (Hint: Recall that for small .) Also, for short wavelengths, show that your formula goes to 0.

4b) Integrating over all frequencies gives the total energy/volume. Do this to show that the energy/volume in a black "cavity" is proportional to T^4. What is the proportionality constant, numerically (in eV/m^3/K^4)?

Hint: .

5a) Warmup Computer Assignment. You may use any programming or graphics system you like - you will probably find Mathematica (henceforth "MMA",) the simplest, and I encourage you to use it. Please turn in a neat, printed output (e.g. a MMA notebook) including titles and explanatory text where appropriate. Before printing your output, please delete any experimentation/dead ends/thrashing around that you did. An independent party should be able to understand, and even run what you hand in to reproduce the results.

Generate a graph of the spectral energy density as a function of frequency, , for T=2.7 K, the temperature of our universe. Chose your range appropriately, so you can clearly see the "whole" curve. Label your plot and axes.

(The curve you generate has been experimentally measured by the COBE satellite to very high accuracy. It fits like a charm!)

Hint: If you plug in MKS values, you will find that the energy density is an incredibly tiny number. So small, MMA will have problems labelling the y axis. A trivial way to avoid this is to multiply the function you're plotting by an appropriately large number, and relabel the plot by hand accordingly. To plot in MMA, you need to give a range of x values: Plot[function[x],{x,xmin,xmax}, AxesLabel -> {"x axis", "y axis"}];

In this case, you might look at the formula and convince yourself that small frequency is when , large frequency is when , and when you're probably somewhere in the middle of the interesting part of the curve...

5b) Post a short message to our newsgroup, "cu.classes.phys2170", which is found from our 2170 WWW page by clicking on "News, Questions, Comments, Discussion - from you". Please be sure you include your name in your message! Some suggestions: if you have your own home page, or want to show off an especially cool one you've found, post its address. If you've found a typo in any of my 2170 home pages, or if you have a suggestion or comment for the class, or a question you think other students might be able to answer, post it. Take a look at the newsgroup - if someone else has already posted a question you can answer, or a comment you'd like to respond to, do that!

Note: There's an extra credit problem for this homework set on the 2170 home page.

Extra Credit problem

Go to Prof. Pollock's home page.

Go to the Physics Department's home page.