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Particle accelerators Edexcel International A Level Physics revision

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In plain words

To see inside a proton you have to hit it very hard, and that means getting particles up to enormous speeds. Electric fields do the speeding up. Magnetic fields do the steering. A linac does it in a straight line, and a cyclotron in a spiral.

4 things to know

  1. Thermionic emission: a heated metal gives off electrons. They can then be accelerated by a p.d., each gaining an energy of qV. For an electron starting from rest, ½mv² = eV (at speeds well below the speed of light).
  2. Linac (linear accelerator): the particles pass through a row of tubes connected to an alternating p.d. They are accelerated by the electric field in each gap between tubes. The tubes get longer along the row, so that the particles, which are getting faster, spend the same time in each one and stay in step with the alternating p.d.
  3. Cyclotron: two hollow D-shaped electrodes sit in a uniform magnetic field. The field bends the particles round in semicircles, and an alternating p.d. between the Ds accelerates them each time they cross the gap. As they speed up their path gets wider, so they spiral outwards.
  4. In a magnetic field of flux density B, a particle of momentum p and charge Q moves in a circle of radius r = p ÷ BQ.

Worked example

An electron is accelerated from rest through a p.d. of 2000 V. Find its speed. (Mass of an electron = 9.11 × 10⁻³¹ kg.)

  1. Energy gained = eV = 1.60 × 10⁻¹⁹ × 2000 = 3.2 × 10⁻¹⁶ J.
  2. ½mv² = 3.2 × 10⁻¹⁶, so v² = 2 × 3.2 × 10⁻¹⁶ ÷ 9.11 × 10⁻³¹ = 7.0 × 10¹⁴.
  3. v = 2.7 × 10⁷ m/s.

Tips and tricks

  • Electric fields change a particle's speed. Magnetic fields only change its direction, because the force is always at right angles to the motion.
  • In a cyclotron the time for each half-turn stays the same as the particles speed up, so the alternating p.d. can keep one frequency.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Particle accelerators: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What is thermionic emission?
    • the release of electrons from a heated metal (the answer)
    • the release of electrons by light
    • the release of alpha particles by a nucleus
    • the release of heat by a current

    Heating gives some electrons enough energy to escape.

  2. What does the magnetic field do in a cyclotron?
    • It bends the particles into a circular path. (the answer)
    • It speeds the particles up.
    • It makes the particles.
    • It stops the particles.

    A magnetic force is at right angles to the motion, so it only steers.

  3. Where are the particles accelerated in a linac?
    • in the gaps between the tubes (the answer)
    • inside the tubes
    • at the source only
    • at the target

    Inside a tube there is no electric field.

  4. The momentum of a particle moving in a fixed magnetic field doubles. What happens to the radius of its path?
    • It doubles. (the answer)
    • It halves.
    • It stays the same.
    • It becomes four times bigger.

    r = p ÷ BQ.

  5. How much energy does an electron gain when it is accelerated through a p.d. of 500 V?
    • 500 eV (the answer)
    • 500 J
    • 1.6 × 10⁻¹⁹ J
    • 500 MeV

    One electronvolt for each volt.

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