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 m(e).

Explanation:

If the photons got frequency w, the energy of each photon must be

,

so the total energy of the system must be

.

The momentum for each photon will be:

.

But, as they are colliding head on, the total momentum of the system must be zero.

Now, for the particles, the energy must be

.

Momentum conservation implies that the total momentum must be zero, so:

,

so the squares of the momentum will be the same.

Now, this implies that the energies for the electron and the positron must be the same, so we can write:

.

Taking conservation of energy in consideration:

.

.

.

.

.

.

.

And this its the electron's momentum

answer(20) psi;