Two photons collide and create an electron-positron pair:
y1+y2 -> e-+e+
If the wavelength of y1 is 1 mm calculate the energy threshold for photon y1 to produce the electron-positron pair.
Suppose E(y1)=hc/[itex]\lambda[/itex]2 where [itex]\lambda[/itex]2 =1.1 mm
Hints: In the center of mass frame of reference, in which the total momentum is 0, the threshold reaction would just produce the two particles at rest. Then in the frame with photon energies E1
and E2 , the two particles would have the same momentum.
Photon Energy=pc where p=momentum
The Attempt at a Solution
The energy of y2 is planck's constant*c/1.1 mm = 1.81*10-22 Joules
I'm a bit confused about where to go from here. Seeing as how energy and momentum are conserved the total energy of y1 and y2 will have to equal the energy of the electron-positron pair. Since I have E(y2) and need to find E(y1) I need to find the energy of the electron-positron pair.
I'm given the energy equation for the electron and their mass, c, and p should all be equal so their energies will be equal.
Is the following assumption correct?
The problem is I don't have a wavelength to figure the energy of the resulting electron-positron pair.