Alpha, beta and gamma radiationAQA A-Level Physics: Revision notes

Alpha (α) particles are helium nuclei (2 protons and 2 neutrons, charge +2e). They are strongly ionising, have a range of a few centimetres in air and are stopped by paper or skin.

Beta-minus (β⁻) particles are fast electrons (charge −e) emitted from the nucleus. They are weakly ionising compared with alpha, have a range of about a metre in air and are stopped by a few millimetres of aluminium.

Gamma (γ) rays are high-energy electromagnetic waves with no charge. They are very weakly ionising, very penetrating, and are never completely absorbed, only reduced by thick lead or concrete.

Alpha and beta particles are deflected in opposite directions by magnetic and electric fields; gamma rays are not deflected.

A GM tube measures count rate. First measure the background count rate with no source, over a long time, and subtract it from all readings. Then place absorbers between the source and tube:

• count rate falls with paper: alpha is present
• count rate falls with a few mm of aluminium: beta is present
• count rate falls only with thick lead: gamma is present

A source that emits several radiations shows these steps in turn.

Gamma rays spread out from a point source in all directions, so the intensity falls with the square of the distance $x$ from the source:

$I = \frac{k}{x^2}$

So doubling the distance makes the intensity one quarter. Count rate (corrected for background) is proportional to intensity, so $C \propto 1/x^2$.

To verify it (Required practical 12), measure the corrected count rate at several distances with a GM tube and metre rule. A graph of $C$ against $1/x^2$ is a straight line through the origin. Alternatively a graph of $\ln C$ against $\ln x$ has a gradient of $-2$.

Background radiation is always present. Its origins include:

• radon gas released from rocks such as granite (the largest natural contribution in the UK)
• rocks and soil, and building materials
• cosmic rays from space
• food and drink, which contain radioactive isotopes such as potassium-40
• artificial sources, such as medical X-rays and nuclear fallout

It is eliminated from calculations by measuring the count rate with the source absent, averaging over a long time because decay is random, and subtracting this from each reading.

Thickness measurement: a beta source is used for paper or aluminium foil, since the count rate depends on thickness. Gamma sources are used for thick steel plates. Alpha is unsuitable because it is completely absorbed.

Safe handling of sources:

• store them in lead-lined containers
• handle them with long tongs, never directly
• limit the time of exposure and work as far away as possible
• wear dosimeter badges to monitor the dose

Medicine: gamma rays destroy cancer cells in radiotherapy, and gamma emitters are used as tracers for diagnosis. The treatment ionises healthy cells too, so there is a risk, but the benefit of treating a serious disease outweighs it. The dose is minimised and directed at the tumour.

A gamma source gives a corrected count rate of 450 min⁻¹ at 0.20 m. What is the count rate at 0.50 m?

$k = Cx^2 = 450 \times 0.20^2 = 18$ min⁻¹ m²

$C = k/x^2 = 18/0.50^2 = 72$ min⁻¹

If the tube also records a background of 20 min⁻¹, the reading seen would be 92 min⁻¹.