Homework 2 Solution

# 37 106 js1 problem 3 ryden 24 first we set the sum m

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Unformatted text preview: o the time for the CMB to raise your temperature by one nanoKelvin is: ∆t = Mc ∆ T 50kg · 4200J kg−1 K−1 · 1 × 10−9 K = = 22.4 s L￿ 9.37 × 10−6 Js−1 Problem 3 (Ryden 2.4) First we set the sum M = m(νe ) + m(νµ ) + m(ντ ) and use the two mass diﬀerence equations given in the problem to express the sum in terms of only one of the neutrino masses. m(ντ )2 c4 = 3 × 10−3 eV 2 + m(νµ )2 c4 = 3.05 × 10−3 eV 2 + m(νe )2 c4 ￿ ￿ ￿￿ ￿￿ eV eV M = m(νe ) + 3.05 × 10−3 + m(νe )2 + 5 × 10−5 + m( ν e ) 2 2 c c2 At this point we should take the derivative of the sum with respect to m(νe ) and set the derivative to zero to solve for the value of m(νe ) that minimizes the sum. But we can skip that by seeing that this function is a monotonically increasing function of m(νe ), meaning that the minimum of the sum occurs at m(νe ) = 0. Then, the mass values that minimize the sum of the masses, M , are: m( ν e ) = 0 eV c2 eV c2 eV m(ντ ) = 5.5 × 10−2 2 c m(νµ ) = 7.1 × 10−3 Problem 4 (Ryden 3.2) Ryden gives...
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## This document was uploaded on 03/31/2014 for the course PHYS 3022.001 at Minnesota.

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