An electron-positron pair traveling towards each other with a speed of 0.95 c with respect to their center of mass,collide and annihilate according to e^- + e⁺ $\rarr$ $\gamma$ + $\gamma$.Assuming the observer is at rest with respect to the center of mass of the electron-positron pair,what is the wavelength of the photons? A)340 fm B)380 fm C)760 fm D)1200 fm E)2400 fm

Question

Quizplus · Accepted Answer

The total momentum of the electron-positron pair is zero before the collision, therefore the total momentum of the photons after the collision must also be zero. This means that the photons must be emitted in opposite directions. 
Using conservation of energy, the total energy of the electron-positron pair before the collision is equal to the total energy of the two photons after the collision. 
The rest energy of the electron and positron is E = mc^2 = 2(0.511 MeV) = 1.022 MeV. 
The total energy of the electron-positron pair before the collision is 2E = 2.044 MeV. 
Using the formula E = hc/λ, where h is Planck's constant and c is the speed of light, we can solve for the wavelength of the photons: 
2.044 MeV = hc/λ
λ = hc/2.044 MeV
Substituting h = 4.136 x 10^-15 eV s and c = 3 x 10^8 m/s, we get λ = 760 fm. 
Therefore, the answer is C.

An Electron-Positron Pair Traveling Towards Each Other with a Speed →\rarr→

An Electron-Positron Pair Traveling Towards Each Other with a Speed $\rarr$