Chapter 28, Problem 52PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
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 Ï€âˆ’mesonis 139.6â€‰MeV.
• The rest mass energy of muon is 105.7â€‰MeV.

Formula used:

Formula to find Î³for muon:

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

â€ƒâ€ƒEkâ€‰=â€‰(mÏ€c2â€‰âˆ’mÎ¼c2)â€ƒâ€ƒâ€ƒâ€ƒâ€ƒâ€ƒâ€ƒâ€ƒEquation-1

Here, mÎ¼is the mass of muon and mÏ€is the mass of Ï€âˆ’mesonand cis the speed of light.

Formula to find the kinetic energy of particle is,

â€ƒâ€ƒEkâ€‰=(Î³âˆ’1)mÎ¼c2(Î³âˆ’1)=â€‰EkmÎ¼c2Î³â€‰=â€‰EkmÎ¼c2+1 â€ƒâ€ƒâ€ƒâ€ƒâ€ƒâ€ƒEquation-2

Formula to find the velocity of electron is,

â€ƒâ€ƒvâ€‰=â€‰c1âˆ’1Î³2

Here, cis the speed of light and Î³is the gamma value of electron

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