Discussion ProblemsDue in section for weeks of Nov 1, and Nov 9, 2009Problem 1Discussion Problems # 97C staffApril 5, 2006Problem 1Find the solid angle (angular area) subtended by a sphere by computing the following integral:Ωsphere=dΩ =2π0π0sinθdθdφ.Problem 2Positronium is an exotic atom that consists of an electron and a positron orbiting one another.a) Derive the reduced mass for positronium.b) Derive the Bohr radius and allowed energies for positronium. (Hint: Be sure to use the results of parta).)c) How do the typical sizes of hydrogen and positronium compare? To answer this find the ratio,a0p/a0H,wherea0pis the Bohr radius of positronium anda0His the Bohr radius of hydrogen.Problem 3Tipler 4-56If electric charge did not exist and electrons were bound to protons by the gravitational force to formhydrogen, derive the corresponding expressions fora0andEnand compute the energy and frequency oftheHαline and the limit of the Balmer series. Compare these with the corresponding quantities for “real”
This is the end of the preview.
access the rest of the document.