How much total energy has each of the two decay particles?
How much 3-momentum does each of the two decay particles have if they are photons?
How much would it be if each of them are (anti-)electrons, at a mass of 0.511.106
eV/c^2 each
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Answers & Comments
In the absence of other information, we assume we are in the frame of reference of the initial particle (i.e. treat the π⁰ as initially at rest before decay).
I’ll assume 140.106 eV/c² means 140x10⁶ eV/c² = 140MeV/c²
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1) Rest-energy of a π⁰ = m₀c² = 140MeV/c² x c² = 140MeV (just needed to change units).
Each of the decay particles must have half the rest energy of the π⁰.
Energy of each decay particle = 140MeV/2 = 70MeV
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2) The momentum of a photon is p = E/c.
p = 70MeV / c = 70MeV/c (just needed to change units).
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3) Electron rest mass m₀= 0.511MeV/c²
E² = p²c² + (m₀c²)²
70² = p²c² + (0.511)²
The electron’s total energy (70MeV) is much bigger than its rest-energy (0.511MeV). So (m₀c²)² is negligible compared to E².
p²c² = 4899.7
. . . .= 4900 near enough
pc = 70MeV
p= 70MeV/c
So the momentum is (practically) identical to the photon’s momentum in part 2).