1. (1 pt) Show from the relativistic velocity transformation equation that if something is moving with velocity c in some direction in one reference frame O', then it is also moving with c in a frame in which O' is moving with speed u in the same direction.

2. (1 pt) A spaceship moving at velocity 0.7c with respect to the earth launches a rocket moving in the same direction at a speed of 0.5c with respect to the spaceship. How fast is the rocket moving with respect to the earth?

3. ( 2pts) A radioactive uranium nucleus (mass 238.0508 amu) can decay to a thorium nucleus (mass 234.0436 amu) and an alpha particle (mass 4.0026 amu) where an amu (atomic mass unit) is equal to 1.661 x 10^-27kg. What is the total kinetic energy of the particles produced in the decay?

4. (2 pts) Light of wavelength 155nm shines on polycrystalline silver (work function = 4.26 eV). What is the maximum kinetic energy of the electrons ejected from the silver?

5. (1 pt) Let's calculate the de Broglie wavelength of a tiny particle much bigger than an atom: What is the wavelength of a bacterium of mass ~10^-15 kg moving at 0.1 microns per second? Would you expect to see quantum interference effects in bacteria?

6. (1 pt) What is the minimum kinetic energy that an alpha particle moving toward a gold nucleus in Rutherford scattering would need in order to come within 20 fm (1 fm = 10^-15m) of the nucleus?

7. (2 pts) An electron in a hydrogen atom makes a transition from an n=3 to an n=4 state.

a. Is this process accompanied by the emission or absorption of a photon?

b. What is the wavelength of the photon?