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 the photon must have to interact with matter and produce a proton-antiproton pair is approximately 1.88 x 10^9 eV.

Step-by-step solution

Understanding the energy-mass relation

According to Einstein's famous equation, energy (E) and mass (m) are related by the equation E = mc^2, where c is the speed of light. In this exercise, we are given a photon (with a certain energy) that interacts with matter to produce a proton-antiproton pair. To determine the minimum energy the photon must have, we must first find the energy required to produce the masses of the proton and antiproton.

Determine the mass of a proton and an antiproton

A proton and an antiproton have the same mass. The mass of a proton (m_p) is approximately 1.6726 x 10^{-27} kg.

Calculate the energy required to produce the proton-antiproton pair

We can use Einstein's equation (E = mc^2) to calculate the total energy (E_total) required to produce a proton-antiproton pair. E_total = 2 × m_p × c^2, where m_p is the mass of a proton and c is the speed of light (approximately 3.0 x 10^8 m/s). E_total = 2 × (1.6726 x 10^{-27} kg) × (3.0 x 10^8 m/s)^2 E_total ≈ 3.0 x 10^{-10} J It's worth noting that energy is usually expressed in electron volts (eV) when dealing with subatomic particles. To convert the energy from Joules to electron volts, we divide by the elementary charge (e ≈ 1.602 x 10^{-19} C): E_total ≈ (3.0 x 10^{-10} J) / (1.602 x 10^{-19} C) ≈ 1.88 x 10^9 eV

Determine the minimum energy the photon must have

The minimum energy the photon must have to produce a proton-antiproton pair is equal to the total energy required to produce the pair. So, the minimum energy of the photon is: E_photon_min ≈ 1.88 x 10^9 eV Thus, the minimum energy the photon must have to interact with matter and produce a proton-antiproton pair is approximately 1.88 x 10^9 eV.