   Chapter 28, Problem 52PE

Chapter
Section
Textbook Problem

A π -meson is a particle that decays into a muon and a massless particle. The π -meson has a rest mass energy of 139.6 MeV, and the muon has a rest mass energy of 105.7 MeV. Suppose the π -meson is at rest and all of the missing mass goes into the muon's kinetic energy. How fast will the muon move?

To determine

The velocity of muon.

Explanation

Given info:

• The rest mass energy of πmesonis 139.6MeV.
• The rest mass energy of muon is 105.7MeV.

Formula used:

Formula to find γfor muon:

The kinetic energy of muon is found by finding missing mass it is given by the expression,

Ek=(mπc2mμc2)        Equation-1

Here, mμis the mass of muon and mπis the mass of πmesonand cis the speed of light.

Formula to find the kinetic energy of particle is,

Ek=(γ1)mμc2(γ1)=Ekmμc2γ=Ekmμc2+1       Equation-2

Formula to find the velocity of electron is,

v=c11γ2

Here, cis the speed of light and γis the gamma value of electron

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