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-kilometer-long Stanford Linear Collider at SLAC (Stanford Linear Accelerator Laboratory) produces a beam of 50.0-GeV electrons. If there are 15,000 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 . 3 6 × 1 0 kg
  • B 2 . 5 5 × 1 0 kg
  • C 1 . 6 8 × 1 0 kg
  • D 2 . 1 9 × 1 0 kg
  • E 1 . 9 0 × 1 0 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 10 GeV converts its energy into particles with masses averaging 200/𝑐MeV.

How many particles are created?

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

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

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

Q5:

In a supercollider at CERN, protons are accelerated to a velocity of 0.230𝑐.

What are the protons’ wavelengths at this speed?

What is the protons’ kinetic energy at this speed?

  • A 3 . 1 5 × 1 0 J
  • B 5 . 7 1 × 1 0 J
  • C 2 . 2 2 × 1 0 J
  • D 2 . 1 4 × 1 0 J
  • E 3 . 9 7 × 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=2.00×10.

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

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

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

Q8:

A charged particle in a 3.5 T magnetic field is bent in a circle of radius 83 cm. What is the magnitude of the momentum of the particle?

Q9:

Protons in a 1.50 km diameter synchrotron can travel at 0.98𝑐. What time is required for a proton to complete one cycle of the synchrotron at this speed?

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

Q10:

The Tevatron at Fermilab was a particle accelerator that could accelerate protons to speeds where the total energy of a single proton was 2.00 TeV.

What is the Lorentz factor for a proton with this total energy? The rest mass of a proton is 938 MeV/c2.

If a 𝜋 were produced that moved at the same speed as one of these protons, what would be the mean lifetime of the pion as measured in the rest frame of the laboratory? A 𝜋 has a mean lifetime of 2.60×10 s in its rest frame.

  • A 4 . 1 6 × 1 0 s
  • B 3 . 9 2 × 1 0 s
  • C 5 . 5 4 × 1 0 s
  • D 7 . 3 3 × 1 0 s
  • E 7 . 7 6 × 1 0 s

How far would such a pion travel in this time?

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