# Homework Help: Relativity question -- an electron e− and a positron e+ collide, annihilate, and produce Bosons...

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1. Jun 6, 2017

### David0709

1. The problem statement, all variables and given/known data
In a particle physics lab, an electron e− and a positron e+ collide, annihilate, and produce a W+ boson and a W− boson. Just before the collision, the electron and positron have a total energy of E = 100 GeV each, with velocities pointing along the +x-axis and -x-axis respectively.

1. What is the momentum p of each of the W bosons after the collision?
2. Relevant equations
me− = me+ = 0.511 MeV/c^2, mW− = mW+ = 80.385 GeV/c^2, E = γmc^2, E^2 = (pc)^2 + (mc^2)^2.

3. The attempt at a solution

Energy conserved so total energy is 200 GeV.

Since they are going in opposite directions and have opposite directions the γ of both electron and position must be identical since they both have the same mass and same total energy. Therefore their speeds must be identical.
Similarly this would suggest that the momentum of both particles must be equal and opposite and so the total momentum before collision is zero.

Using E ^2 = (pc)^2 + (mc^2)^2
Yields a momentum of 3.17 * 10^-17 of both Bosons (but both in different directions)

Could anyone please confirm whether my solutions are correct.

Last edited by a moderator: Jun 6, 2017
2. Jun 6, 2017

### TheReal NdGT

Momentum and energy must be conserved, as you said, so the answer is correct

3. Jun 7, 2017

### vela

Staff Emeritus