Question

A muon and an antimuon are moving in opposite directions with velocities of -0.4 c and 0.4 c, respectively. When they collide, they can annihilate each other and turn into two photons. Both muon and antimuon have a mass of 105.66 MeV/c2.

What is the total energy before the collision?

What is the energy of each photon?

What is the wavelength of each photon?

Answer 1

Use:

$E=Gmc^{2}\rightarrow G=\frac{1}{\sqrt{1-0.4^{2}}}=1.09$

$E=1.09(155.66)\rightarrow E=169.67\: MeV\: for\: each\: muon$

Total energy is

----------------------------------------------

Each photon gets half the total energy

-----------------------------------------------

$E=\frac{hc}{wl}\rightarrow wl=\frac{ 6.62x10^{-34}*3X10^{8}}{169.67x10^{6}*1.6x10^{-19} }$

$wl=7.316X10^{-15}m$