Question

An electron-positron pair (positron is electron’s antiparticle, it has the same mass as electron, but opposite charge) can be produced what two photon are collided. Two photons of frequency ω are collided head-on. What will be the electron’s momentum? Electron’s rest mass is me

Problem 4. Electron-positron production An electron-positron pair (positron is electron's antiparticle, it has the same mass as electron, but opposite charge) can be produced what two photon are collided. Two photons of frequency w are collided head-on. What will be the electron's momentum? Electron's rest mass is me.

Answer 1

et So the process is shown below, y ---> é (phoron) (Photon) (elee ton) (poneitron) Let E, and Er are the energian sif election and positron respectively. Then 5,9 = b + me? where pe- and bet an the momentums.of election and position respectively. Hence, E-EEkeberg 645) (E-E). O and & - Pezi + mesy Again, the frequencies of the photom are equal. Thus from Energy conservation law, we have aħw E + E + 2 mec? (6+5) = 2(*w-moc?) - © Therefore, from-O, we get 2 3 E-6 = 2{tits - mec) Since the photons have same frequency thom their wavelengtha aho be equal. Therefore, the momentum of the combination of two photons, travelling along the opposite direction is 2010, and according to the momentum conservation law, the momentum combi- anation of the electron -position system, is also refore, Pe-+ber -0.= ha Then from – ③ we have E,-E2s From the combination of equation- and 9, we zero. There have, 2E, = sw-mer) Ei= tw-mec2 Hence, the momentom of electron e's be E,?- mezcy **?4m%! 2 hwmae? - mala bet = t ² ² - 2ħw mec? 2 2 be- | 2w²-2ho mee? momentum of eletron

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