PHYSICS 131 hw-5-soln

PHYSICS 131 hw-5-soln - HOMEWORK SET 4, PHYS. 131...

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HOMEWORK SET 4, PHYS. 131 Instructor: Anthony Zee Email: zee@kitp.ucsb.edu TA: Matt Pillsbury Email: mtp@physics.ucsb.edu Problem 9.1. An advanced civilization living outside a spherical neutron star of mass M constructs a massless shell concentric with the star such that the area of the inner surface is 144 πM 2 and the area of the outer surface is 400 2 . What is the physical thickness of the shell? Using (9.5) on p.187, we Fnd that the inner radius of the shell is 6 M and the outer radius is 10 M . The distance between the radii is then ± 10 M 6 M dr g rr = ± 10 M 6 M dr ² r r - 2 M = ³ 4 5 - 2 6 + log ´ 27 + 12 5 15 + 6 6 µ¶ M 4 . 64 M As you can see, the Fnal integral is a bit ugly; I did it with Mathematica. Problem 9.2. Positrons are produced in the dense plasma surrounding a neu- tron star, which is accreting material from a binary companion, and electrons and positrons annihilate to produce γ rays. Assuming the neutron star has a mass of 2 . 5 M ± (solar masses) and a radius of 10 km, at what energy should a distant observer look for the γ rays begin emitted from the star by this process?
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This note was uploaded on 07/15/2008 for the course PHYS 131 taught by Professor Kevin during the Spring '08 term at UCSB.

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PHYSICS 131 hw-5-soln - HOMEWORK SET 4, PHYS. 131...

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