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iloveannaw
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Homework Statement
A photon decays into a positron and an electron - show why this is impossible. Under what conditions could this be possible?
Homework Equations
conservation of linear momentum:
[tex] P_{PHOTON} = P_{POSITRON} + P_{ELECTRON} [/tex]
conservation of energy:
[tex] E_{PHOTON} = E_{POSITRON} + E_{ELECTRON} [/tex]
The Attempt at a Solution
[tex] P_{PHOTON} = P_{POSITRON} + P_{ELECTRON} [/tex]
[tex] \frac{E_{PHOTON}}{c} = \gamma mu + \gamma mu = 2\gamma mu [/tex][tex] E_{PHOTON} = E_{POSITRON} + E_{ELECTRON} [/tex]
[tex] E_{PHOTON} = \gamma mc^{2} + \gamma mc^{2} = 2\gamma mc^{2} [/tex]
[tex] \frac{E_{PHOTON}}{c} = 2\gamma mu = \frac{2\gamma mc^{2}}{c} [/tex]
therefore:
[tex] u = c [/tex] …which would be impossible. is this right? I'm a bit confused on how you apply conservation of energy and momentum in relativity. for instance i haven't considered any reference frames here and I'm not sure if it requires some kind of transformation.
any help is appreciated, thank you!
btw I've assumed that the product particles have equal rest mass and share the energy equally. and u is the velocity of the positron/ electron
Homework Statement
Homework Equations
The Attempt at a Solution
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