1. Considering Yukawa's hypothesis that the nuclear force should be due to the exchange of massive particles (that he called mesons), calculate the expected mass of this hypothetical meson.
2. Draw a table showing all the elementary spins 1/2 anti-particles arranged in three families horizontally with the individual members of each family vertically. In the table give the names, symbols, electric charges and approximate masses of each anti-particle.
3. In a unit system where c=h=1, the Compton wavelength for an muon is given by λμ= mμ-1 calculate the numerical value.
In the same system, the Bohr radius of a muonic hydrogen atom is given by rB = α(mμ) where α is the fine structure constant α= 1/137, calculate the numerical value. [A muonic hydrogen atom is just equivalent to a regular hydrogen atom but the electron is substituted by a muon].
4. The weak interaction is assumed to be due to W or Z exchange. If the Z has a mass of 90 GeV/c^2, calculate the range of the weak interactions. How does this compare with the size of a nucleon? What are the consequences for the likelihood of nuclear beta decay.
5. Two protons are separated by a distance of 10^-15m. Calculate (a) the electric force and (b) the gravitational force on one proton due to the other. Using the relative strengths of the strong, electromagnetic, weak and gravitational forces, estimate (c) the strong force and (d) the weak force between the two protons.
Summarize the four results in order of increasing strength.