Question

A photon can interact with matter by producing a proton-antiproton pair. What is the minimum energy the photon must have?

Short answer

Answer: The minimum energy a photon must have to interact with matter and produce a proton-antiproton pair is approximately 3 x 10^-10 Joules.

Step-by-step solution

Understand the process

A photon can interact with matter and produce a proton-antiproton pair. In this process, the energy of the photon must be sufficient to create the two particles, which have minimum rest mass. The energy conversion occurs according to the mass-energy equivalence principle.

Mass-energy equivalence

According to the mass-energy equivalence principle, the energy of a particle (E) is directly related to its mass (m) by the equation: E = mc^2 where c is the speed of light (approximately 2.998 x 10^8 m/s).

Calculate the energy required to create a proton-antiproton pair

Since a proton and an antiproton have the same mass, we only need to find the mass of a proton and multiply it by 2. The mass of a proton is approximately 1.67 x 10^-27 kg. Using the mass-energy equivalence equation, we can calculate the energy needed to create one proton: E_proton = (1.67 x 10^-27 kg) * (2.998 x 10^8 m/s)^2 To determine the energy needed to create a proton-antiproton pair, we multiply the energy needed to create one proton by 2: E_pair = 2 * E_proton

Calculate the minimum energy for the photon

The minimum energy required for the photon to create a proton-antiproton pair is equal to E_pair. Therefore, we just need to compute E_pair with the numbers: E_pair = 2 * (1.67 x 10^-27 kg) * (2.998 x 10^8 m/s)^2 ≈ 3 x 10^-10 J So, the minimum energy the photon must have to interact with matter and produce a proton-antiproton pair is approximately 3 x 10^-10 Joules.