Finding the Centre of Mass Speed for a High and Low Energy Photon Collision

[albega]

Homework Statement

High energy photon of energy E collides with a low energy photon of energy 1eV. It forms an electron-positron pair. I have found the threshold energy as E=261GeV.

I am asked to find the speed of the centre of mass at this threshold energy.

Homework Equations

E=γmc²

The Attempt at a Solution

I can use conservation of energy to get the energy of the electron (or positron) say then use the above formula to find v from γ. I believe this then should be the CM speed. However it returns c. I don't believe that this is an acceptable solution (I don't have the answers though). Any thoughts would be helpful, thanks.

 

[albega]

Homework Statement

High energy photon of energy E collides with a low energy photon of energy 1eV. It forms an electron-positron pair. I have found the threshold energy as E=261GeV.

I am asked to find the speed of the centre of mass at this threshold energy.

Homework Equations

E=γmc²

The Attempt at a Solution

I can use conservation of energy to get the energy of the electron (or positron) say then use the above formula to find v from γ. I believe this then should be the CM speed. However it returns c. I don't believe that this is an acceptable solution (I don't have the answers though). Any thoughts would be helpful, thanks.

I realize it may be a bit vague. Just in case, the full question is

A high-energy photon γ₁ of energy E traveling through space interacts with an
infra-red photon γ₂ of energy 1 eV to produce an electron-positron pair via the reaction
γ₁+γ₂→e^-+e⁺
By considering the total energy and the total momentum show that the threshold value of E required for this process is 261 GeV.

What is the velocity of the centre of mass at this threshold?

I have the 261GeV, but can only get speed c for the second bit (as outlined in my original post).