Worksheet: Particle Accelerators and Detectors

In this worksheet, we will practice describing the interactions of particles with high energy accelerators and particle detectors.

Q1:

The 3.20-km-long Stanford Linear Collider at SLAC (Stanford Linear Accelerator Laboratory) produces a beam of 50.0-GeV electrons. If there are 1 5 0 0 0 accelerating tubes, what average voltage must be across the gaps between them to achieve this energy?

Q2:

A proton and an antiproton are at rest relative to an observer. The proton and antiproton annihilate, completely destroying both masses and creating two photons of equal energy. What is the characteristic 𝛾 -ray energy you would look for if searching for evidence of this annihilation?

Q3:

Assume that beam energy of an electron-positron collider is approximately 4.73 GeV. What is the total mass of a particle produced in the annihilation of an electron and positron in this collider?

  • A 2 . 1 9 × 1 0 2 6 kg
  • B 1 . 9 0 × 1 0 2 6 kg
  • C 2 . 3 6 × 1 0 2 6 kg
  • D 1 . 6 8 × 1 0 2 6 kg
  • E 2 . 5 5 × 1 0 2 6 kg

Q4:

The intensity of cosmic ray radiation decreases rapidly with increasing energy, but there are occasionally extremely energetic cosmic rays that create a shower of radiation from all the particles they create by striking a nucleus in the atmosphere. Suppose a cosmic ray particle having an energy of 1 0 1 0 GeV converts its energy into particles with masses averaging 2 0 0 𝑐 M e V 2 .

How many particles are created?

  • A 3 × 1 0 1 0
  • B 2 × 1 0 1 0
  • C 6 × 1 0 1 0
  • D 5 × 1 0 1 0
  • E 8 × 1 0 1 0

If the particles rain down on a 1.00-km2 area, how many particles are there per square meter?

  • A 5 × 1 0 4
  • B 2 × 1 0 4
  • C 7 × 1 0 3
  • D 1 × 1 0 4
  • E 4 × 1 0 4

Q5:

In a supercollider at CERN, protons are accelerated to a velocity of 0 . 2 3 0 𝑐 .

What are the protons’ wavelengths at this speed?

What is the protons’ kinetic energy at this speed?

  • A 3 . 9 7 × 1 0 J
  • B 5 . 7 1 × 1 0 J
  • C 3 . 1 5 × 1 0 J
  • D 2 . 2 2 × 1 0 J
  • E 2 . 1 4 × 1 0 J

Q6:

In a particle accelerator, the energy of an electron is 57.0 GeV.

Find the Lorentz factor 𝛾 for the electron.

Find de Broglie’s wavelength of the electron.

Q7:

The Stanford linear accelerator (SLAC) can produce a Lorentz factor 𝛾 = 2 . 0 0 × 1 0 .

What is the effective accelerating potential for the electrons of SLAC?

  • A 1 . 2 0 × 1 0 V
  • B 2 . 6 0 × 1 0 V
  • C 1 . 0 5 × 1 0 V
  • D 1 . 0 2 × 1 0 V
  • E 1 . 3 1 × 1 0 V

What is the total energy, in giga-electron volts, of the electrons accelerated by SLAC?

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