- #1

kreil

Gold Member

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## Homework Statement

A photon of energy E strikes an electron at rest and undergoes pair production, producing a positron and an electron:

photon + (e-) = (e+) + (e-) + (e-)

The two electrons and the positron move off with identical momenta in the direction of the initial photon. Find the kinetic energy of the three final particles and find the energy E of the photon.

## Homework Equations

1.[tex]K=E-E_0[/tex]

2.[tex]E_0=mc^2[/tex]*rest energy of photon = 0.

3.[tex]E=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]

4.[tex]E=\sqrt{(pc)^2+(mc^2)^2}[/tex]

5.[tex]p_i=p_f=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]

## The Attempt at a Solution

The initial momentum of the photon is mc, and this gives an initial kinetic energy of 2mc

^{2}. This is equal to the final kinetic energy, and since each particle has the same momentum then the kinetic energy of each is 2mc

^{2}/3.

My problem comes with finding the energy of the photon. The book gives an answer of 4mc

^{2}, and I'm not sure how to get that. Any help is appreciated.

Josh