PHY357S: Monday, 31 March 1997

Problem Set 5

due Friday, 11 April 1997

(Note: As long as I find it under my door by 11am Monday morning, it will count as being on time.)

These questions are based on both the lectures and the text.
If you have any questions about these problems, ask me.
You can contact me at dbailey@physics.utoronto.ca, Room 919, or at 978-4993.

Each problem is of equal weight, but not all problems may be marked.

Problems

(1) The Cabibbo-Kobayashi-Maskawa mixing matrix describes the mixing between the mass and weak eigenstates of quarks:

where cij=cosqij and sij=sinqij. Current measurements tell us that sinq12=0.221, sinq23=0.04, and sinq23=0.003. We also know that the b quark is much heavier than the c quark, but their lifetimes are almost the same.

Why is the b quark lifetime not much shorter than the c quark lifetime?

(2) (a) Why is the neutron heavier than the proton?

(b) Why is the p+ meson heavier than the p0 meson?

(3) (a) Modify the Bethe-Weizäcker semiempirical mass formula (F&H equation 16.9) to include a gravitational binding energy term

(b) A neutron star is a humongous stable nucleus made only of neutrons (see F&H Section 19.5). Use your answer to part (a) to estimate the minimum mass of a nucleus made only of neutrons. Give your answer in both atomic mass units and in solar mass units (see F&H Appendix A2). (Note: The minimum mass for making a neutron star depends on the mass necessary to drive the collapse of the star, and so may differ from the minimum mass of neutron supernucleus you have calculated.)