Muon Speed Calculation After Photon Collision

[J_M_R]

Homework Statement

Two equal-energy photons collide head-on and annihilate each other, producing a u+ and u- pair. The muon mass is about 207 times the electron mass. Calculate the maximum wavelength of the photons for this to occur.
If the photons have this wavelength, describe the motion of the u+ and u- immediately after they are produced.
What is the speed of each muon after they have moved apart? Use correct relativistic expressions for momentum and energy.

Homework Equations

E=hc/lambda
E=mc^2

The Attempt at a Solution

For the first part, m(u)=207m(e) and so lambda=hc/207m(e)*c^2 = 1.17x10^-14m

I thought the motion would be that the muons will move in opposite directions with equal speeds - apparently not?

I am not sure how to approach the final part.

Thanks in advance for your help!

 

[vela]

Homework Statement

Two equal-energy photons collide head-on and annihilate each other, producing a u+ and u- pair. The muon mass is about 207 times the electron mass. Calculate the maximum wavelength of the photons for this to occur.
If the photons have this wavelength, describe the motion of the u+ and u- immediately after they are produced.
What is the speed of each muon after they have moved apart? Use correct relativistic expressions for momentum and energy.

Homework Equations

E=hc/lambda
E=mc^2

The Attempt at a Solution

For the first part, m(u)=207m(e) and so lambda=hc/207m(e)*c^2 = 1.17x10^-14m

Can you explain your reasoning here in a bit more detail?

I thought the motion would be that the muons will move in opposite directions with equal speeds - apparently not?

I am not sure how to approach the final part.

Thanks in advance for your help!