Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.

• In most of this chapter we treated the atomic nucleus as fixed. This approximation (often a very good one) can be avoided by using the reduced mass, as described in connection with Equations (5.31) and (5.32). (a) What percent error do we make in the energy levels of ordinary hydrogen when we treat the proton as fixed? (b) Answer the same question for muonic hydrogen, which is a negative muon bound to a proton. (See Problem 1.)

Problem 1

•• The negative muon is a subatomic particle with the same charge as the electron but a mass that is about 207 times greater: mμ ≈ 207 me. A muon can be captured by a proton to form a “muonic hydrogen atom,” with energy and radius given by the Bohr model, except that me must be replaced by mμ. (a) What are the radius and energy of the first Bohr orbit in a muonic hydrogen atom? (b) What is the wavelength of the Lyman α line in muonic hydrogen? What sort of electromagnetic radiation is this? (Visible? IR? etc.) Treat the proton as fixed (although this is not such a good approximation here — see the above problem).