- #1
buttermellow7
- 10
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Homework Statement
Why can't a 3.141 MeV photon decay spontaneously into an electron and positron, each with rest mass energy .511 MeV?
Homework Equations
Conservation of Momentum and Energy
[tex] E=\sqrt{m^2c^4+p^2c^2} [/tex]
[tex] E_\gamma=pc [/tex]
The Attempt at a Solution
[tex] 3.141=\sqrt{(.511)^2+p^2c^2} [/tex]
[tex] \pm\sqrt{9.866-.261}/c=p [/tex]
[tex] p_e=\pm \frac{3.099}{2} eV/c [/tex]
[tex] p_\gamma=3.141 eV/c [/tex]
[tex] 3.141\neq 3.099 \neq 0 [/tex]
Is this correct? Am I allowed to assume that the momenta of the positron and electron are equal? My feeling in a qualitative perspective is that you could find a frame of reference in which the net velocity of the electron-positron pair is zero, but the velocity of the photon is never zero in any frame. However, my prof told me that gamma ray photons do decay into electrons and positrons? What's the dealio?