IB DP Physics: HL复习笔记12.1.6 Pair Production & Annihilation

Pair Production & Annihilation

Annihilation

  • When a particle meets its antiparticle pair, the two will annihilate
  • Annihilation is:

When a particle meets its equivalent anti–particle they both are destroyed and their mass is converted into energy in the form of two gamma ray photons

7.-Annihilation

When an electron and positron collide, their mass is converted into energy in the form of two photons emitted in opposite directions

  • The minimum energy of one photon after annihilation is the total rest mass energy of one of the particles is:

Emin = hfmin = E

  • Where:
    • Emin = minimum energy of one of the photons produced (J)
    • h = Planck's Constant (J s)
    • fmin = minimum frequency of one of the photons produced (Hz)
    • E = rest mass energy of one of the particles (J)
  • To conserve momentum, the two photons will move apart in opposite directions
  • To conserve energy, the two photons will have the same energy, which means they also have the same frequency because

E = hf

Pair Production

  • Pair production is the opposite of annihilation
  • Pair production is:

When a photon interacts with a nucleus or atom and the energy of the photon is used to create a particle–antiparticle pair

  • The presence of a nearby neutron is essential in pair production so that the process conserves both energy and momentum
  • A single photon alone cannot produce a particle–anti-particle pair or the conservation laws would be broken
  • Pair creation is a case of energy being converted into matter

2.2.5.-Pair-Production

When a photon with enough energy interacts with a nucleus it can produce an electron-positron pair

  • This means the energy of the photon must be above a certain value to provide the total rest mass energy of the particle–antiparticle pair
  • The minimum energy for a photon to undergo pair production is the total rest mass energy of the particles produced:

Emin = hfmin = 2E

  • Where:
    • Emin = minimum energy of the incident photon (J)
    • h = Planck's Constant (J s)
    • fmin = minimum frequency of the photon (Hz)
    • E = rest mass energy of one of the particles (J)
  • To conserve momentum, the particle and anti–particle pair move apart in opposite directions
  • Remember for both calculations, the frequency f is also defined by the wave equation, v = fλ
  • Using this equation, the wavelength λ can also be calculated
    • Remember that v is c (the speed of light) for gamma ray photons

Worked Example

Calculate the maximum wavelength of one of the photons produced when a proton and antiproton annihilate each other.

2.1.5-Annihilation-Worked-Example

Exam Tip

Since the Planck constant is in Joules (J) remember to always convert the rest mass-energy from MeV to J.

 

 

 

 

 

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