M Go Review Conceptual Example 7 as background for this...

$\mathrm{M}$ Go Review Conceptual Example 7 as background for this problem. An electron and its antiparticle annihilate each other, producing two $\gamma$ -ray photons. The kinetic energies of the particles are negligible. Determine the magnitude of the momentum of each photon.

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Key Concepts

Relativistic Energy-Momentum Relationship

For massless particles like photons, the energy and momentum are directly related by the equation E = pc. This relationship allows one to determine the momentum of a photon if its energy is known.

Mass-Energy Equivalence

Stemming from Einstein’s famous equation E = mc², mass-energy equivalence explains how the rest mass of particles can be converted into energy. In annihilation events, the entire rest mass of the electron and its antiparticle is transformed into photon energy.

Conservation of Energy

In any closed system, the total energy must remain constant. In particle annihilation processes, the sum of the rest mass energies (and any kinetic energies) of the annihilating particles is converted entirely into the energy of the resulting photons.

Conservation of Momentum

Momentum is conserved in all physical processes. When an electron and its positron annihilate, not only is energy conserved, but the net momentum before annihilation (often zero in a symmetric case) must equal the net momentum after, which governs the directional properties and magnitudes of the photon momenta.

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