PH422: Nuclear Physics
Homework II
Due January 31
1. (F-H 5.5) Assume that the electron and muon are uniform spheres. Compute the
radius (classically)
q 3 such that the speed of the surface caused by the rotation with angular
momentum 4 h is equal to the speed of light, c.
2. (F-H 5.6) Consider a system consisting of two identical particles and assume that the
total wave function is of the form:
(~x1 ; ~x2 ) = A (~x1 )(~x2 ) + B (~x2 )(~x1 ):
where and are orthonormal functions. Find the values of A and B that make the total
wave function normalized to unity and (a) symmetric, (b) antisymmetric, or (c) neither
under interchange of labels (1,2).
3. Look up the necessary masses and calculate the Q-values for each of the following
reactions. (For exothermic reactions Q gives the energy released; for endothermic reactions
-Q gives the (CM) threshold energy for the reaction.)
+ p ! K 0 + 0
K + p ! 0 + 0
222
Rn !218 Po + 6
Li + d !7 Li + p
Check that the conservation laws of electric charge, fermion number, and baryon and lepton
number are satised throughout.
4. (F-H 5.18) How can the stability of electrons be measured? Try to design a simple
experiment and estimate the limit on the lifetime that you expect to get from your experiment. (Hint: imagine what would happen if one of the electrons in a sample of matter
were to suddenly decay.)
5. (a) Explain how 14 C is used to date organic material (look it up). (b) What is the age
of a carbon sample which has a 14 C/12 C ratio of 1 10 13 ? (c) How can such small ratios
be measured?
6. (F-H 5.29) The exchange of a rho meson between nucleons is believed to contribute to
the nuclear force. Estimate the range of this force and compare it with the range obtained
by the exchange of a pion.
7. (F-H 5.34) A beam of pions is incident on a stationary hydrogen target. Find the
threshold pion kinetic energy for the reaction + p ! 0 + K 0 (i.e. the pion kinetic
energy in the laboratory at which the reaction begins to occur?)