Relativity with energy and momentum question

[StonedPhysicist]

Here is the question, I was able to complete part a and b but c has beaten me!

A pi meson has rest mass 131 MeVc^-2 and total energy 1.000 GeV

a) What is its momentum, expressed in MeVc^-1
For this I obtained 991 MeVc^-1 using the equation E²=c²p²+M²c⁴

b) By how much is its speed less than c?
Using γ=E/mc² i got a value of γ = 7.63 so therefore this system is highly relativistic then subbed this into γ=1/√(1-v²/c²) to get an answer of 2.57x10⁶ ms^-1 less than c.

c) This is the one i am stuck on: The pi meson decays in flight into two photons. Find the maximum and minimum energies (in MeV) possible for the photons in the coordinate system (or reference frame) of the observer who measures this total energy, and the minimum and maximum wavelengths corresponding to these energies.

I do not quite understand what it means by or how to get the maximum and minimum energies. I would of assumed both photons get half the total energy and half the total momentum each.

 

[mfb]

In the rest frame of the pion, the decay is symmetric, but in the lab frame (where the pion is moving) it can be asymmetric. The two photons can have different angles relative to the pion flight direction.

 

[StonedPhysicist]

In the rest frame of the pion, the decay is symmetric, but in the lab frame (where the pion is moving) it can be asymmetric. The two photons can have different angles relative to the pion flight direction.

I don't see how this will give them different energies though?

 

[StonedPhysicist]

could it be a doppler effect?

 

[mfb]

I don't see how this will give them different energies though?

Imagine one flying in the pion flight direction and one backwards. If they would have the same energy and momentum, total momentum would be zero after the decay but non-zero before. A violation of momentum conservation.

It is related to the Doppler effect, but formulas for that are impractical here.