Particle accelerators and detectorsEdexcel International A Level Physics: Revision notes

When a metal filament is heated, some of its conduction electrons gain enough kinetic energy to escape from the surface. This is thermionic emission. The apparatus must be evacuated so that the electrons are not scattered by air and the filament does not burn away.

A charged particle in a uniform electric field is accelerated by the force $F = QE$. If a particle of charge $Q$ is accelerated from rest through a potential difference $V$ it gains kinetic energy

$\frac{1}{2}mv^2 = QV$

For electrons accelerated through 1500 V: $v = \sqrt{\frac{2eV}{m}} = \sqrt{\frac{2 \times 1.60 \times 10^{-19} \times 1500}{9.11 \times 10^{-31}}} = 2.3 \times 10^{7}$ m s⁻¹.

A magnetic field exerts a force $F = BQv$ perpendicular to the velocity of a charge moving at right angles to the field. The force does no work, so the speed does not change, but the direction does. The particle is accelerated (its velocity changes) and moves in a circle.

The magnetic force provides the centripetal force:

$BQv = \frac{mv^2}{r}$ so $r = \frac{mv}{BQ} = \frac{p}{BQ}$

The radius is proportional to the momentum and inversely proportional to $B$ and $Q$. A particle with twice the charge and the same momentum moves on a circle of half the radius.

A linac has a line of hollow metal drift tubes in a vacuum, joined alternately to the terminals of a high-frequency alternating supply.

• the electric field in the gaps accelerates the charged particles
• inside a tube there is no field, so the particles move at constant speed
• the p.d. reverses while the particles are inside a tube, so they are accelerated again at the next gap
• the particles move faster, so the tubes get longer: each tube takes half a period of the supply

Particles are accelerated in a straight line, so no magnetic field is needed.

A cyclotron has two hollow D-shaped metal dees in a vacuum with a small gap between them. A uniform magnetic field acts perpendicular to the dees and an alternating p.d. is applied across the gap.

• particles are accelerated by the electric field each time they cross the gap
• inside each dee there is no electric field; the magnetic field bends the path into a semicircle
• as the speed rises, $r = \frac{mv}{BQ}$ increases, so the particles spiral outwards
• the time per semicircle $\frac{\pi r}{v} = \frac{\pi m}{BQ}$ is constant, so the frequency of the supply, $f = \frac{BQ}{2\pi m}$, can stay fixed

The particles leave at the edge with the maximum radius.

Charged particles passing through a detector (for example a cloud chamber, bubble chamber or Geiger tube) ionise the atoms along their path, leaving a visible or measurable trail.

• a perpendicular magnetic field deflects the particles; the direction of curvature shows the sign of the charge
• the radius of curvature gives the momentum, using $r = \frac{p}{BQ}$
• a particle that loses energy by ionisation slows down, so its track spirals inwards
• neutral particles leave no track, as they do not ionise directly