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WeekProb_Nov1_Nov9 - Discussion Problems 9 7C sta sta 2006...

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Discussion Problems Due in section for weeks of Nov 1, and Nov 9, 2009 Problem 1 Discussion Problems # 9 7C staff April 5, 2006 Problem 1 Find the solid angle (angular area) subtended by a sphere by computing the following integral: Ω sphere = d Ω = 2 π 0 π 0 sin θdθdφ. Problem 2 Positronium 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 part a).) c) How do the typical sizes of hydrogen and positronium compare? To answer this find the ratio, a 0 p /a 0 H , where a 0 p is the Bohr radius of positronium and a 0 H is the Bohr radius of hydrogen. Problem 3 Tipler 4-56 If electric charge did not exist and electrons were bound to protons by the gravitational force to form hydrogen, derive the corresponding expressions for a 0 and E n and compute the energy and frequency of the H α line and the limit of the Balmer series. Compare these with the corresponding quantities for “real”
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