Elementary particles：練習問題

In a pair production process, a single photon interacts with a nucleus to produce an electron-positron pair. Which condition must be satisfied for this to occur?

The rest energy of a proton is \(938\text{ MeV}\). What is the minimum frequency of a single photon required to produce a proton-antiproton pair?
Use \(h = 6.63 \times 10^{-34}\text{ J s}\) and \(1\text{ eV} = 1.60 \times 10^{-19}\text{ J}\).

Which of the following correctly identifies the charge and mass of an antineutron compared to a neutron (mass \(m_n\))?

A photon with an energy of \(2.50\text{ MeV}\) undergoes pair production to create an electron and a positron. What is the total kinetic energy of the two particles immediately after production?
(Rest energy of an electron = \(0.51\text{ MeV}\))

Which of the following physical quantities is different for a proton and an antiproton?

Explain why a single photon cannot undergo pair production in a vacuum without the presence of a nearby nucleus.

A photon with an energy of \( 2.40 \text{ MeV} \) undergoes pair production to create an electron-positron pair. Determine the maximum possible kinetic energy of the positron, in MeV, if the energy is shared equally between the two particles.

An electron and a positron annihilate to produce two identical photons. Calculate the energy of each photon in MeV and explain why they must move in opposite directions.

A free neutron decays into a proton, an electron, and an antineutrino.

(a) Write the balanced nuclear equation for this decay and identify the type of interaction responsible.
(b) Describe the change in quark composition during this process.
(c) Explain why the existence of the neutrino was first hypothesised to explain the observations of beta decay.

A high-energy photon interacts with a nucleus, resulting in pair production where an electron and a positron are created.

(a) Describe the process of pair production and state the necessary condition for it to occur.
(b) Calculate the minimum frequency of a photon required to produce an electron-positron pair.
(Rest mass energy of an electron = \( 0.511 \text{ MeV} \); \( 1 \text{ eV} = 1.60 \times 10^{-19} \text{ J} \); Planck constant \( h = 6.63 \times 10^{-34} \text{ Js} \)).
(c) If the photon energy is greater than the minimum required, what happens to the excess energy?