Pion decays into gamma rays. Find the energy and angle

[Executionator]

Hi all,

I was having trouble with this problem and hoping that someone could help me with it.

A pion has a rest energy of 135 MeV. It decays into two gamma rays, bursts of electro magnetic radiation that travel at the speed of light. A pion moving through the laboratory at v = 0.97c decays into two gamma rays of equal energies, making equal angles θ with the direction of motion. Find the angle θ and the energies of the two gamma rays. (Hint: gamma rays are electromagnetic radiation with E = pc.)

I am pretty sure I will be using conservation of relativistic energy and momentum but I am still confused.

I know that E=γmc^2 and P=γmv

I find gamma 1/sqrt(1-(0.97c)^2/c^2)≈ 4.11

I know that mc^2= 135MeV

With this I get E=(4.11)(135MeV)≈ 555.32MeV

For P I get (4.11)m(0.97c)=3.99mc≈ 538.66MeV/c

I am a bit unsure what to do next with this.

 

[petergreat]

This post should be moved to "Special & General Relativity" subforum. It's a simple exercise in special relativity, and doesn't really require knowledge of particle physics.

 

[AdrianTheRock]

Boost yourself into the pion's rest frame, then back again afterwards?