9.2 Atoms and nuclear radiation — Learn

Prerequisites: Section 9.1, especially the particles in the nucleus and the meaning of the mass number and the atomic number.

By the end of this section you can: describe radioactive decay and the radiation it emits; write balanced nuclear equations; explain what half-life means and use it to find a count rate; and compare contamination with irradiation.

1. Unstable nuclei and radioactive decay

Some nuclei are unstable. An unstable nucleus gives out radiation as it changes to become more stable. This is called radioactive decay.

Radioactive decay is a random process. You cannot predict which nucleus will decay next, or when it will happen. The decay of one nucleus does not change the chance that another nucleus will decay.

2. Activity and count rate

Activity is the rate at which the unstable nuclei in a source decay. It is measured in becquerels (Bq), where one becquerel is one decay each second.

A detector, such as a Geiger-Muller tube, records a count rate: the number of decays it detects each second. Some radiation is absorbed before it reaches the detector, so the count rate is usually smaller than the activity.

3. The radiation a nucleus can emit

A nucleus can emit four kinds of nuclear radiation.

Radiation	What it is	Stopped by	Range in air	Ionising power
Alpha ( $\alpha$ )	Two protons and two neutrons; the same as a helium nucleus	Paper or skin	A few centimetres	Strongest
Beta ( $\beta$ )	A fast electron ejected from the nucleus	A few millimetres of aluminium	About a metre	Weaker than alpha
Gamma ( $\gamma$ )	Electromagnetic radiation from the nucleus	Thick lead or concrete	Very long; passes through the body	Weakest

A nucleus can also emit a neutron. You will meet neutrons again in Section 9.4, where they keep a chain reaction going.

The ionising power matters. Ionising radiation can knock electrons away from the atoms it passes through, which can damage living cells. Alpha particles are the most strongly ionising, but they are stopped quickly. Gamma rays are the least ionising, but they penetrate the furthest.

4. Nuclear equations

A nuclear equation shows the change in the nucleus. Two rules always hold:

the mass numbers on the two sides must balance;
the atomic numbers on the two sides must balance.

An alpha particle is written $^{4}_{2}\alpha$ , and a beta particle is written $^{0}_{-1}\beta$ .

In alpha decay, the nucleus loses two protons and two neutrons, so the mass number falls by 4 and the atomic number falls by 2. In beta decay, a neutron turns into a proton, so the mass number does not change and the atomic number goes up by 1. A gamma ray has no mass and no charge, so it changes neither number.

Worked example 1. Radon-222 decays by alpha emission. Write the balanced nuclear equation.

Radon-222 is $^{222}_{86}\text{Rn}$ . The mass number falls by 4 to give 218, and the atomic number falls by 2 to give 84.

^{222}_{86}\text{Rn} \rightarrow {}^{218}_{84}\text{Po} + {}^{4}_{2}\alpha

Worked example 2. Carbon-14 decays by beta emission. Write the balanced nuclear equation.

Carbon-14 is $^{14}_{6}\text{C}$ . The mass number does not change, and the atomic number goes up by 1 to give 7.

^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + {}^{0}_{-1}\beta

5. Half-life

The half-life of a radioactive isotope is the time it takes for:

the number of nuclei of the isotope in a sample to halve; or
the count rate from a sample to fall to half of its starting level.

Worked example 3. A source has a count rate of 400 counts per second. The count rate is measured every 2 minutes: 400, 200, 100, 50. Work out the half-life.

The count rate halves from 400 to 200 in 2 minutes, and then from 200 to 100 in the next 2 minutes. The half-life is 2 minutes.

The half-life is a statistical average. It describes a very large number of nuclei. A single measurement will not fall to exactly half, because the decay is random.

Worked example 4. A tracer has a half-life of 6.0 hours and an initial count rate of 800 counts per second. Calculate the count rate after 12 hours.

\frac{12}{6.0} = 2 \ \text{half-lives}

After one half-life the count rate is 400 counts per second. After two half-lives it is 200 counts per second.

\text{count rate} = \frac{800}{2^2} = 200 \ \text{counts per second}

6. Net decline after a number of half-lives

Sometimes a question gives the number of half-lives and asks for the net decline in the emission, written as a ratio.

After $n$ half-lives, the fraction of the original activity that remains is

\left(\frac{1}{2}\right)^{n}

so the net decline is $1 - \left(\dfrac{1}{2}\right)^{n}$ .

Worked example 5. After three half-lives, calculate the net decline in the emission as a ratio.

After three half-lives the fraction remaining is $\left(\dfrac{1}{2}\right)^3 = \dfrac{1}{8}$ .

\text{net decline} = 1 - \frac{1}{8} = \frac{7}{8}

The net decline is a ratio of $7:8$ of the original emission.

7. Contamination and irradiation

Two words describe two different hazards.

Contamination is the unwanted presence of radioactive atoms on or in another material. The contaminating atoms keep decaying, so the material itself gives out radiation.
Irradiation is exposing an object to nuclear radiation. The irradiated object does not become radioactive, because the radiation passes through it or is absorbed.

Alpha contamination inside the body is very serious, because alpha particles have a short range and are strongly ionising. In that short range, they transfer a lot of energy to living cells. Gamma irradiation from a source outside the body is the opposite case: gamma rays penetrate the body, so they can reach living cells from outside.

Watch out. After two half-lives the source has not gone. One half-life leaves one half of the activity, two half-lives leave one quarter, and three half-lives leave one eighth. The activity keeps halving and never reaches zero in a fixed time. Re-check by halving the starting value once for each half-life, rather than stopping early.

8. Try it: how a count rate falls

The figure shows how the count rate of a source falls with time. You can change the half-life and the starting count rate.

Predict first. Do not move the sliders yet. Write down your answers.

After three half-lives, what fraction of the starting count rate is left?
Does the curve reach zero? Explain your answer.

Test. Set the half-life to 6 hours and the starting count rate to 800 per second. Read the count rate at 6, 12, 18 and 24 hours. Then change the half-life to 3 hours and read the same four times again.

Explain. Each value is half the one before, so the curve gets close to zero but never reaches it. Why does a real measurement of a count rate only follow this curve roughly? Write your answer in two or three sentences, using the word random.

9. Progress check

Return to the chapter problem. The tracer has a half-life of 6.0 hours and a starting count rate of 800 counts per second. A sample is prepared at 08:00. Work out the count rate at 20:00 the same day.

You should now be able to

describe radioactive decay and explain why it is random;
define activity and state its unit;
describe alpha, beta and gamma radiation, and compare their penetration, range and ionising power;
write balanced nuclear equations for alpha decay and beta decay;
explain what half-life means, and use it to find a count rate or an activity;
compare contamination with irradiation, and describe the hazard of each.