9.2 Atoms and nuclear radiation — Practise

Work through these on your own. Keep your working neat, and keep the units with your numbers. Questions marked H are for Higher tier.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

Define activity, and state the unit in which it is measured.
Describe an alpha particle, a beta particle and a gamma ray, and say where each one comes from.
State which type of radiation is stopped by a sheet of paper, and which type needs thick lead to stop it.
A nucleus of radon-222, $^{222}_{86}\text{Rn}$ , emits an alpha particle. Write the balanced nuclear equation for the decay.
A nucleus of carbon-14, $^{14}_{6}\text{C}$ , emits a beta particle. Write the balanced nuclear equation for the decay.
A source has a half-life of 4.0 minutes and starts with a count rate of 640 counts per second. Calculate the count rate after 12 minutes.
A source has a count rate of 200 counts per second. After 30 minutes the count rate is 50 counts per second. Work out the half-life of the source.
Explain why the count rate from a source does not fall to exactly half after one half-life.
Explain why the mass number of a nucleus does not change when the nucleus emits a beta particle.
Compare the hazards of contamination and irradiation, and state one precaution that protects against each.
A source has an activity of 2.5 kBq. Convert this to becquerels.
H After four half-lives, state the fraction of the original activity that remains.
H After three half-lives, calculate the net decline in a radioactive emission as a ratio.

Answers and concise solutions

1. Activity and its unit

Activity is the rate at which the unstable nuclei in a source decay.
Activity is measured in the becquerel, Bq. One becquerel is one decay each second.

2. Alpha, beta and gamma radiation

An alpha particle is two protons and two neutrons, the same as a helium nucleus. It is emitted from the nucleus.
A beta particle is a fast electron ejected from the nucleus when a neutron turns into a proton.
A gamma ray is electromagnetic radiation emitted from the nucleus, with no mass and no charge.

3. Stopping alpha and gamma radiation

Alpha radiation is stopped by a sheet of paper. It has a range of only a few centimetres in air and is strongly ionising.
Gamma radiation needs thick lead, or thick concrete, to reduce it. It has a very long range in air and is weakly ionising.

4. The balanced alpha decay equation

Answer: An alpha particle is $^{4}_{2}\alpha$ . The mass number falls by 4 to give 218, and the atomic number falls by 2 to give 84. The equation is $^{222}_{86}\text{Rn} \rightarrow {}^{218}_{84}\text{Po} + {}^{4}_{2}\alpha$ .

5. The balanced beta decay equation

Answer: A beta particle is $^{0}_{-1}\beta$ . The mass number does not change, so it stays at 14. The atomic number rises by 1 to give 7. The equation is $^{14}_{6}\text{C} \rightarrow {}^{14}_{7}\text{N} + {}^{0}_{-1}\beta$ .

6. Count rate after 12 minutes

Answer: $12\,\text{min} \div 4.0\,\text{min} = 3$ half-lives. The count rate is $\dfrac{640}{2^3} = 80$ counts per second.

7. Half-life of the source

Answer: The count rate falls from 200 to 100, and then from 100 to 50. That is two half-lives in 30 minutes, so the half-life is $\dfrac{30}{2} = 15$ minutes.

8. Why the count rate is only about half

Radioactive decay is a random process. You cannot predict which nucleus will decay next, or when.
The half-life is the average time for half of the nuclei to decay. A real measurement follows this average only roughly.

9. Why beta decay leaves the mass number unchanged

In beta decay a neutron in the nucleus turns into a proton, so the number of nucleons does not change.
A fast electron is ejected, but an electron has no protons and no neutrons, so the mass number stays the same.

10. Contamination compared with irradiation

Contamination is the unwanted presence of radioactive atoms on or in a material. The hazard lasts as long as the source stays there, because it keeps decaying inside or on the material.
Irradiation is exposing an object to radiation. The hazard lasts only while the source is nearby, and the object does not become radioactive.
Protect against contamination with gloves and by keeping sources sealed. Protect against irradiation by keeping sources at a distance, limiting the time near them and using shielding.

11. The activity in becquerels

Answer: The prefix kilo means $1000$ , so $2.5\,\text{kBq} = 2.5 \times 1000 = 2500\,\text{Bq}$ .

12. Fraction of activity remaining

Answer: Each half-life halves the activity, so after four half-lives the fraction remaining is $\left(\dfrac{1}{2}\right)^4 = \dfrac{1}{16}$ .

13. Net decline after three half-lives

Answer: After three half-lives the fraction remaining is $\left(\dfrac{1}{2}\right)^3 = \dfrac{1}{8}$ . The net decline is $1 - \dfrac{1}{8} = \dfrac{7}{8}$ , a ratio of $7:8$ of the original emission.