1. Between faraway galaxies, an intergalactic train five light seconds (that is, 15.10⁸ meters) long is zipping past a space station at a speed of 0.8c. The train is, naturally, fully equipped with synchronized clocks. As the front of the train passes the space station, both the clock on the station and the one on the front of the train read zero.

(a) Working in the frame of reference of the space station, figure out what the station clock reads as the back of the train passes the space station.

(b) What would an observer on the space station figure out that the clock on the front of the train must be reading at the instant that the back of the train is passing the space station?

(c) Still working in the frame of reference of the space station, what does the clock at the back of the train read at the instant the back of the train passes the space station?

(d) Now start again, working in the frame of reference of the train. Calculate the reading on the space station clock, and that on the clock at the back of the train, at the instant they pass each other. That is, at the instant when the back of the train is passing the space station.

(e) Suppose that at the instant that the back of the train passes the space station, observers on the station and on the back of the train simultaneously take telephotos of the clock at the front of the train. Would you expect the photos to both show the clock reading the same time? Comment briefly.

2. If two protons collide with sufficient energy, they can produce an antiproton (together with another proton)

(a) Working in the center of mass frame, find the minimum kinetic energy for this reaction to occur.

(b) Find the speed of the protons in the center of mass frame just before the reaction.

(c) In the lab frame, one of the initial protons (the target) is at rest. Find the speed of the other one, and deduce its kinetic energy.

3. (a) Describe briefly, with a diagram, how the photoelectric effect can be used to determine Planck’s constant.

(b) For a clean sodium surface, radiation of wavelength 253 nm corresponds to a stopping potential of 2.6 volts, and radiation at 330nm needs 1.47 volts. What value of Planck’s constant follows from these data?

(c) Will red light cause a photocurrent with a sodium cathode? (Base your reply on a calculation with the numbers from (b).)

(d) For the 253 nm radiation in (b), what is the maximum speed with which electrons leave the sodium surface?

4. (a) Explain how analysis of the black body radiation from an oven at low frequencies could be used to find Boltzmann’s constant.

(b) What range corresponds to "low frequencies" in (a)? Explain.

(c) Assuming the earth is a perfect black body, and that sunlight delivers one kilowatt per square meter (for area perpendicular to the incoming sunlight). Assume further that all the earth’s surface is at the same temperature, the sun is the only source of heat, and the radiated heat from the earth balances the incoming energy from the sun. What is the earth’s temperature? (Stefan’s constant = 5.67.10^-8.)

5. (a) Describe in a couple of sentences how X-rays were discovered.

(b) Describe briefly how radioactivity was discovered.

(c) X-rays and radioactivity will ionize a gas. Explain how this ionization differs from that in a liquid undergoing electrolysis. What, if anything, does it tell us about the structure of the atom?

(d) How and approximately when was the relativistic increase in mass with speed first detected?

(e) It was thought at first that alpha particles were uncharged. Why?