Alpha, beta and gamma radiation and their properties, the random nature of decay, the decay constant and activity, the exponential decay law, and half-life.

What this dot point is asking

Edexcel wants you to describe alpha, beta and gamma radiation and their properties, explain the random and spontaneous nature of decay, define the decay constant and activity, use the exponential decay law, and work with half-life.

The answer

Types of radiation

The more ionising a radiation, the more rapidly it loses energy and the shorter its range. In magnetic and electric fields, alpha and beta deflect in opposite directions (opposite charges) and gamma is undeflected (no charge).

Random and spontaneous decay

Because decay is random, we work with the average behaviour of huge numbers of nuclei, which gives smooth exponential statistics even though each individual decay is unpredictable. The fluctuations seen on a count-rate meter are direct evidence of this randomness.

Decay constant, activity and the decay law

A larger decay constant means faster decay and a shorter half-life. The exponential form arises because the rate of decay is proportional to the number of nuclei present, $\frac{dN}{dt} = -\lambda N$. Plotting $\ln A$ against $t$ gives a straight line of gradient $-\lambda$, the standard way to find the decay constant experimentally.

Half-life

After $n$ half-lives the activity is $A_0 \times (\frac{1}{2})^n$. Half-lives range from fractions of a second to billions of years, which is what makes some isotopes useful for dating and others for medical imaging.

Examples in context

Carbon-14 dating measures the residual activity of ancient organic material against its known half-life. Smoke detectors use a tiny alpha source (americium-241) whose short range makes it safe behind a screen. Medical tracers such as technetium-99m have short half-lives so they decay away quickly after imaging. Radiotherapy uses penetrating gamma sources to target tumours, and nuclear power monitoring tracks the activity of fission products.

Try this

Q1. State which type of radiation is the most ionising. [1 mark]

• Cue. Alpha radiation.

Q2. A source has a half-life of $4.0$ days and an initial activity of $640$ Bq. Find its activity after $12$ days. [2 marks]

• Cue. Twelve days is three half-lives: $640 \rightarrow 320 \rightarrow 160 \rightarrow 80$ Bq.

Q3. A sample has decay constant $\lambda = 0.10$ per year. Find its half-life. [2 marks]

• Cue. $t_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{0.10} = 6.9$ years.