Elementary particles：練習問題

Which of the following statements correctly compares an electron and its antiparticle, the positron?

Which of the following statements correctly compares an electron and its antiparticle, the positron?

A gamma-ray photon undergoes pair production to create a particle and its antiparticle. If the rest energy of the particle produced is \( 105.7 \text{ MeV} \), what is the minimum frequency of the photon required?

Take Planck's constant \( h = 6.63 \times 10^{-34} \text{ J s} \) and \( 1 \text{ eV} = 1.60 \times 10^{-19} \text{ J} \).

The rest energy of a proton is approximately \(938\text{ MeV}\). What is the minimum energy of a single photon required to produce a proton-antiproton pair through the process of pair production?

Which of the following describes the conservation of baryon number and lepton number during the beta-plus (\(\beta^+\)) decay of a proton?
The decay is represented as: \(p \rightarrow n + e^+ + \nu_e\)

Explain why a particle and its corresponding antiparticle must produce at least two photons when they undergo annihilation.

Calculate the minimum energy required, in MeV, for a single gamma-ray photon to produce a proton-antiproton pair, given the rest energy of a proton is \(938 \text{ MeV}\).

A hypothetical decay is proposed where a neutron transforms into a positron and an antiproton. By evaluating the conservation of charge, baryon number, and lepton number, explain why this process is strictly forbidden by the laws of particle physics.

(a) Describe the process of pair production and explain why there is a minimum photon energy required for this process to occur.

(b) A photon with energy \(1.50\) MeV interacts with a nucleus to produce an electron-positron pair. Calculate the maximum kinetic energy of the electron produced, assuming the energy is shared equally between the two particles.
(Rest energy of an electron = \(0.511\) MeV)

(c) State the name of the antiparticle for each of the following:
i) Proton
ii) Neutrino

(a) Define annihilation and describe what happens when a proton meets an antiproton.

(b) Calculate the frequency of each of the two identical photons produced when a proton and an antiproton annihilate. Assume both particles are initially at rest.
Rest energy of a proton = \(938\) MeV.
Planck constant \(h = 6.63 \times 10^{-34}\) J s.
Elementary charge \(e = 1.60 \times 10^{-19}\) C.

(c) Discuss how the laws of conservation of baryon number and conservation of lepton number apply to this annihilation interaction.