- #1

Phynos

- 31

- 4

## Homework Statement

A pion at rest (m

_{π}= 273m

_{e}) decays into a muon (m

_{μ}= 207m

_{e}) and an antineutrino (m

_{n}≈ 0).

Find (a) the kinetic energy of the muon and (b) the energy of the antineutrino in electron volts.

## Homework Equations

K = (γ-1)mc

^{2}

E = γmc

^{2}

E

_{R}= mc

^{2}

E

^{2}= p

^{2}c

^{2}+ (mc

^{2})

^{2}

I didn't use all of these, but I'm assuming a solution requires one or more of them.

## The Attempt at a Solution

Not really sure how to go about this when the mass of the neutrino is so close to zero. If I assume the total energy after the reaction of the neutrino is essentially zero, then the missing energy goes into the motion of the muon.

K

_{μ}≈ E

_{Rπ}- E

_{Rμ}

= c

^{2}(m

_{π}- m

_{μ})

= c

^{2}(0.511*10

^{6}eV/c

^{2})(273-207)

= 3.37*10

^{7}eV

= 33.7 MeV

The answer in the book is 4.08MeV so either my assumption that K

_{n}≈ 0 is a bad one, or I've made a mistake somewhere here.