- #1

Kunhee

- 51

- 2

## Homework Statement

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An electron e- and positron e+ annihilate to produce two photons.

a_ Why are two photons produced rather than one?

b_ Assume that the e- and e+ are at rest just before they annihilate. In their rest frame, what are the energies and momenta of the photons? Define the +x axis to be the direction of motion of one of the photons.

c_ What are the energies and momenta of the photons in another frame that movies with (v/c)^2 = 4/5 with respect to the rest frame?

## Homework Equations

p = y m0 u

E total = y m0 c^2

E rest = m0 c^2

E kinetic = (1-y)(m0 c^2)

## The Attempt at a Solution

a _ I think this is a simple answer that reads "momentum should be conserved after annihilation so there must be two photons created with equal and opposite momentum.

b _ Because the electron and positron are at rest before annihilation, there is no velocity transformation or Lorentz transformation required so should the momentum of the photon be "p = m0 c" and energy be "E =m0 c^2" ?

c _ This time the frame with photons is moving with (v/c)^2 = .8. I am guessing the electron and positron are still at rest before annihilation so there is no velocity transformation necessary. So should the momentum of the photon apply just the Lorentz transformation, making "p = y m0 c" and energy be "E = y m0 c^2" where y is the Lorentz factor with (v/c)^2 = .8 ?

Thanks!