# Pair production problem

1. May 18, 2017

### ikihi

1. The problem statement, all variables and given/known data

A proton and anti-proton are created by a photon with wavelength λ= 6.607×10−7 nm. What is the magnitude of the velocity of the newly created proton and anti-proton pair? Note, the mass of a proton/anti-proton is mp= 1.673×10-27 kg = 938.3M MeV/c2.

2. Relevant equations

Ephoton = h ⋅ c / λ
E0 = m0 ⋅ c2
KE = 0.5 ⋅ m ⋅ v2

3. The attempt at a solution

Ephoton= 3.009 x 10-10 J
E0 = 1.506 x 10-10 J

KE=Ephoton - 2 ⋅ E0 / (2)
KE= 3.009 x 10-10 - 2 ⋅ 1.506 x 10-10 J / (2)
KEof either particle= -1.5 x 10-13 J

Last edited: May 18, 2017
2. May 18, 2017

### Bandersnatch

Google calculator shows 938.3 MeV=1.503E-10 Joules.

3. May 18, 2017

### patric44

if you convert the energy of the photon to Mev and subtract from it (2*938.3 Mev) it will give a positive number
i guss the problem is the mass of the proton missing a lot of digits and the speed of light as well.
like Bandersnatch said if you use the full digits of the mass and speed of light it will give 1.503*10^-10

4. May 18, 2017

### ikihi

I calculated E0 using E0 = m0 ⋅ c2. So is that the same as the given value?

5. May 18, 2017

### ikihi

You are right. I converted both to MeV and it came out to KE = 0.029!

0.029 MeV ---> 4.646 x10-15 J

I calculate that the speed is 2.36 x 106 m/s.

However after using more sig fig digits the answer goes to 0 m/s. Maybe this is a relativistic problem that needs a different equation?

Last edited: May 18, 2017
6. May 18, 2017

### haruspex

That seems rather unlikely. If you cannot find a mistake please post all your working.