   Chapter 11, Problem 82CP ### University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185

#### Solutions ### University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185
Textbook Problem

# In supei novae, neutrinos are produced in huge amounts. They were detected from the 1987A supernova in the Magellanic Cloud, which is about 120,000 light- years away from Earth (relatively close to our Milky Way Galaxy). If neutrinos have a mass, they cannot travel at the speed of light, but if their mass is small, their velocity would be almost that of light, (a) Suppose a neutrino with a 7 − e V / c 2 mass has a kinetic energy of 700 keV. Find the relativistic quantity γ = 1 1 − v 2 / c 2 for it. (b) If the neutrino leaves the 1987A supernova at the same time as a photon and both travel to Earth, how much sooner does the photon arrive? This is not a large time difference, given that it is impossible to know which neutrino left with which photon and the poor efficiency of the neutrino detectors. Thus, the fact that neutrinos were observed within hours of the brightening of the supernova only places an upper limit on the neutrino’s mass. (Hint: You may need to use a series expansion to find v for the neutrino, since its γ is so large.)

To determine

(a)

The relativistic quantity.

Explanation

Given:

γ=1 1 v 2 c 2

KE= 700×103eV

mc2 = 7eVc2

Formula used:

The time taken is calculated by

Δt=trtp

Calculation:

The formula to find the energy is

E=KE+mc2

Here E is the total energy KE is the kinetic energy and mc2 is the rest mass energy.

The total energy is the product of a relativistic number and mass-energy of the neutrino

To determine

(b)

The time taken by the photon to arrive.

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