This preview shows page 1. Sign up to view the full content.
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...
View
Full
Document
This document was uploaded on 03/31/2014 for the course PHYS 3022.001 at Minnesota.
 Spring '14
 Hanany
 Work, Radiation

Click to edit the document details