For ultrarelativistic particles such as photons or high-energy electrons, the relation between energy and momentum is not E=p2/2m but rather E=pc. (This formula is valid for massless particles, and also for massive particles in the limit E≫mc2.)
((a)) Find a formula for the allowed energies of an ultrarelativistic particle confined to a one-dimensional box of length L.
((b)) Estimate the minimum energy of an electron confined inside a box of width 10−15 m. It was once thought that atomic nuclei might contain electrons; explain why this would be very unlikely.
((c)) A nucleon (proton or neutron) can be thought of as a bound state of three quarks that are approximately massless, held together by a very strong force that effectively confines them inside a box of width 10−15 m. Estimate the minimum energy of three such particles (assuming all three of them to be in the lowest-energy state), and divide by c2 to obtain an estimate of the nucleon mass.