END; include ("common_short.php"); physics_header("",""); print <<Physics H133: Problem Set #\$ps_num Here are some hints, suggestions, and comments on the problem set.

## Two-Minute Problems

Remember to give a good explanation, no longer than two sentences.

1. Q8T.7: In which states will the quantons sit if they are bosons (fermions)? Add up the corresponding energy eigenvalues.
2. Q9T.6: Look at the answers to Exercises Q9X.7 and Q9X.8 (page 173) for example explanations.

## Chapter Q8 and Q9 Problems

• Q8S.7: (a) How should you modify Eq.(Q8.7) for helium to account for the modifications in a_0 and E_n? (Don't forget the ke2 part.) (b) Check that n_i=infty produces visible light for n_f=5, and then lower n_i until you reach the edge of the visible spectrum. (c) Try other values of n_f, starting from n_f=1. For each n_f, bring your modified version of Eq.(Q8.7) into a form that allows you to quickly check whether there are any possible n_i-values at all that will produce visible light. If the answer is yes, identify these n_i.
• Q8S.9: Protons and neutrons are commonly called "nucleons". Use the Pauli principle to fill up the box states with either only neutrons or with neutrons and protons until all 12 nucleons are placed in the lowest possible energy eigenstates. Add up the energy eigenvalues for each case and compare.
• Q9S.4: Look up xenon (Xe) in the periodic table on the back inside cover of Unit Q. What is the ground state configuration of its filled electron orbitals? Use Table Q9.3 to explore the possible excited states for one of the 5p electrons and whether any of them are metastable.
• Q9S.7: Draw "before and after" pictures for the emission and absorption processes and consider in each case the constraints from energy and momentum conservation. Convince yourself that in either case the atom suffers recoil, i.e. it ends up with kinetic energy even if before the emission or absorption process it was at rest. Work out the effects of this recoil energy on the energy balance and photon energy.
• Q8R.1: Consider the ratio of the two longest wavelengths in each case. How do they compare with the ratio of the given numbers?