Issued Fri, Jan 17 Due Mon, Jan 27

Required reading so far: F+H Ch. 1-4.

There are HINTS for this homework assignment.

Here, and throughout the semester, please show your work on all problems. Organize your homework so the grader can follow your solution clearly. Explain (in words) what you're doing and what assumptions you make, whenever it seems appropriate.

(Because there are various editions of F+H , which may have different problem numbers, I have paraphrased F+H questions for you)

I have included a few hints here. I anticipate having rather more involved hints early next week. I'll post them on the web.

1) The maximum wavelength of photons that ionize "muonic hydrogen" (that's a proton with a muon circling, rather than an electron) is given in natural units by the formula . (Here, e is the charge of the electron, and is the muon mass.) Find this wavelength in cgs units (i.e. in cm.)

2a) A beam of pi+ ( ) mesons enters a large dipole magnet (uniform B field) with B=10 kgauss. The pion beam curves in a circle of radius 166.7 cm. What is the momentum (in eV/c) and total energy (in eV) of the beam?

2b) How far will the pion track go before its intensity is reduced by 10%?

(See F+H p. 5 for an explanation of mean life. The pi+ mean life is in Table A3)

Hint: Your answer to part a should be somewhere in the neighborhood of 500 MeV, so if you don't get near that, please assume 500 MeV pions in b.

3) F+H 2.24 (a only). ("A beam of 2 TeV electrons runs head on into a beam of 2 TeV protons [Tera is 10^12] What energy would you need to give to an electron beam to get the same center-of-mass energy, if you ran the electron beam into static protons instead?")

(cont. ->)

4) F+H 3.1. ("You have a beam of 100 MeV protons, but you want a beam of 50 MeV protons. So you run them through an absorber. How thick must the absorber be if it's made of carbon, or of lead? (Answer in cm, and g/cm^2)")

I only want a rough estimate, a single significant figure is fine.

(It's fun to think about the "which absorber would be preferable" question, but it is not required.)

Useful facts: density of Pb is 11 g/cc, of C is 2.25 g/cc

5) F+H 3.8 ("A 1 mA beam of 800 MeV protons pass through a 1cm^3 cube of copper. How much energy is deposited per sec in the Cu? If you don't cool it, what's the temperature rise/sec?")

As in the previous problem, I only want a rough estimate, again a single significant figure is fine.

Useful facts: density of copper is 8.9 g/cc,

heat capacity of Cu is 0.093 Cal/[gram (degree Celsius)]

6a) F+H 4.10. ("A scintillation counter counts eight muons/hr, on average. If you run 1000 experiments, each one hour long, how often do you expect you will find runs with a total of 2 counts? (or 4, 7, 8, 16 counts?)" )

I would assume that these cosmic ray muons are randomly Poisson distributed.

6b) F+H 4.15. ("Compute the magnetic energy stored in the Argonne 12 ft bubble chamber. From what height, roughly, would an average car (say, 1 ton) have to be dropped to equal this energy?")

Hint: The chamber's characteristics are given in the very last sentence of section 4.4: B=18 kG, volume is 25 m^3.

Hint: I get several kilometers for the car question!!