One could ?nd the maximum value of the energy of any one photon in the three-pho

Question

One could ?nd the maximum value of the energy of any one photon in the three-photon decay of positronium.

Find the magnitude of the momentum for the third photon in the case where two photons go in one direction and the third goes o? in the opposite direction. Ignore the binding energy of the positronium. The mass of an electron is 0.511 MeV/c2.

Answer in units of MeV/c .

Part 2)
Find the magnitude of the corresponding momentum of any one photon for the symmetric decay, wherein the three photons go o? making a 120? angle with each other.

Answer in units of MeV/c .

Explanation / Answer

Applying the conservation of energy , First we find the mass of the each photon.
m =( 0.511/3 ) MeV/c^2
If two photons going one direction and other going opposite direction
Applying conservation of momentum, P1+P2 = P3
( 0.511/3 ) MeV/c + ( 0.511/3 ) MeV/c = P3
therefore P3 = 0.340 MeV/c

the momentum for the third photon in this case is 0.340 MeV/c
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Part 2,
Applying conservation law of momentum,
sqrt of (P1^2 + P2^2+2P1P2cas120) = P3
sqrt. of (2p1^2+2P1^2(-0.5)) = P3     (since P1 = P2)

P3 = P= 0.170 MeV/c

therefore the momentum of the each photon is 0.170 MeV.

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