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PHYSICS 131 hw-5-soln

# PHYSICS 131 hw-5-soln - HOMEWORK SET 4 PHYS 131 Instructor...

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HOMEWORK SET 4, PHYS. 131 Instructor: Anthony Zee Email: [email protected] TA: Matt Pillsbury Email: [email protected] 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 π M 2 and the area of the outer surface is 400 π M 2 . What is the physical thickness of the shell? Using (9.5) on p.187, we find 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 r r - 2 M = 4 5 - 2 6 + log 27 + 12 5 15 + 6 6 M 4 . 64 M As you can see, the final 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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PHYSICS 131 hw-5-soln - HOMEWORK SET 4 PHYS 131 Instructor...

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