An electron and a positron collide head on, annihilate, and create two 0.755- MeV photons travel

step 1 For this question since the The energy of the two photons must equal the total energy of the two

An electron and a positron collide head on, annihilate, and...

Key Concepts

Particle Annihilation

Annihilation is a process where a particle and its corresponding antiparticle collide and convert their mass into other forms of energy, typically photons. This phenomenon is a prime example of mass-energy equivalence and highlights how the rest mass energy and kinetic energy of the original particles are redistributed into the energy of the emergent photons.

Relativistic Kinetic Energy

When dealing with high-speed particles, their kinetic energy is not simply given by classical formulas but must be evaluated using relativistic equations. In problems like electron-positron annihilation, determining the kinetic energy involves subtracting the well-defined rest mass energy from the total energy, ensuring that both energy and momentum conservation laws are satisfied.

Rest Mass Energy

Every particle possesses an intrinsic energy associated with its rest mass as described by Einstein’s relation E=mc². For electrons and positrons, their rest masses contribute significantly to the total energy budget, and any excess energy observed in the product particles is attributed to the additional kinetic energy present before annihilation.

Conservation of Momentum

Momentum must be conserved in any collision or reaction. In annihilation problems, especially when the reaction produces particles traveling in opposite directions, the vector sum of the momenta of the final particles must equal the total momentum of the initial particles. This is critical when determining the energies and directions of emitted photons.

Conservation of Energy

This principle states that the total energy of an isolated system remains constant over time. In the context of particle collisions and annihilations, the sum of the initial rest energy and kinetic energy of the particles must equal the energy carried away by the products— in this case, the energy of the resulting photons.

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