This note covers background radiation, how radioactivity is detected, the properties of alpha, beta and gamma radiation, nuclear decay equations, half-life calculations and the safe use of radioactive sources. It links atomic structure to real uses in medicine, industry and archaeology.
Key ideas
Radioactive decay. Some nuclei are unstable. They emit radiation to become more stable. Decay is spontaneous, which means it is not affected by outside conditions such as temperature. It is also random: you cannot predict when a particular nucleus will decay, only the chance that it will.
Background radiation. There is always a small amount of ionising radiation around us. Sources include radon gas from rocks and soil, food and drink, cosmic rays from space, and man-made sources such as medical equipment and nuclear waste.
Detection. A Geiger–Müller (GM) tube connected to a counter detects ionising radiation. The reading is a count rate, in counts per second or per minute. Before experiments you measure the background count rate. It is then subtracted from readings to find the corrected count rate due to the source.
The three types of radiation.
- Alpha (α): a helium nucleus (2 protons and 2 neutrons), positively charged. Strongly ionising. Stopped by paper or a few centimetres of air.
- Beta (β): a fast-moving electron from the nucleus, negatively charged. Moderately ionising. Stopped by a few millimetres of aluminium.
- Gamma (γ): electromagnetic radiation of very high frequency. Weakly ionising. Reduced, but not stopped completely, by thick lead or several metres of concrete.
Ionisation means radiation knocks electrons out of atoms to make ions. It is how radiation damages living cells and is also how it is detected.
(Extended) In an electric or magnetic field, the positive alpha particles and the negative beta particles are deflected in opposite directions. Alpha particles are deflected less because they are much more massive. Gamma radiation has no charge and is not deflected.
Changes in the nucleus (extended).
- Alpha decay: the nucleon number goes down by 4 and the proton number goes down by 2.
- Beta decay: a neutron changes into a proton and an electron. The electron is emitted. The nucleon number is unchanged and the proton number goes up by 1.
- Gamma emission: no change to the nucleon number or the proton number. The nucleus loses energy only.
In a decay equation, the nucleon numbers (top) must add up to the same total on both sides, and so must the proton numbers (bottom).
Half-life. The half-life of an isotope is the time taken for half of the unstable nuclei in a sample to decay. It is also the time for the count rate from a sample to fall to half its starting value. After each half-life, the amount remaining halves again: 1, 1/2, 1/4, 1/8 and so on. Half-lives range from tiny fractions of a second to billions of years. The corrected count rate is used when finding half-life from measurements.
Uses. Medical tracers use a gamma source with a short half-life, which passes out of the body and decays quickly. Beta sources are used to monitor the thickness of paper or metal foil, because the count rate changes with thickness. Gamma sources sterilise medical equipment and food. Radioactive dating of old objects uses the half-life of carbon-14, and of rocks uses other isotopes.
Safety. Ionising radiation can damage cells and cause cancer. To reduce risk:
- keep sources in lead-lined containers when not in use;
- keep a large distance from the source, for example by using tongs;
- limit the time of exposure;
- wear protective clothing and monitor exposure with a badge, for people who work with radiation.
Definitions and formulae
| Term or formula | Meaning / when to use |
|---|---|
| Corrected count rate | Measured count rate − background count rate. |
| Half-life | Time for half the unstable nuclei (or the count rate) to fall to half. |
| Alpha decay | A falls by 4, Z falls by 2. |
| Beta decay | A unchanged, Z rises by 1. |
| Remaining fraction | (1/2)n after n half-lives. |
| Ionising | Able to remove electrons from atoms. |
Worked examples
Example 1 A sample has a half-life of 3.0 hours. Its count rate at the start is 640 counts per minute, with negligible background. What is the count rate after 12 hours?
Number of half-lives = 12 ÷ 3.0 = 4.
The count rate halves four times: 640 → 320 → 160 → 80 → 40.
Answer: 40 counts per minute
Example 2 A 48 g sample of a radioactive isotope has a half-life of 6.0 days. How much of the isotope is left after 18 days? Also, a source gives 85 counts per minute with a background of 15 counts per minute. State the corrected count rate.
Number of half-lives = 18 ÷ 6.0 = 3.
Mass: 48 → 24 → 12 → 6.
Corrected count rate = 85 − 15 = 70 counts per minute.
Answer: 6.0 g of the isotope remains. The corrected count rate is 70 counts per minute.
Example 3 (extended) Radium-226 (proton number 88) decays by alpha emission. Write the equation, giving the nucleon and proton numbers of the new nucleus.
An alpha particle is 42He. The nucleon number falls by 4: 226 − 4 = 222.
The proton number falls by 2: 88 − 2 = 86. The element with proton number 86 is radon (Rn).
Check: top 226 = 222 + 4, bottom 88 = 86 + 2.
Answer: 22688Ra → 22286Rn + 42He
Common errors
- Saying that after two half-lives all the sample has decayed. One quarter remains.
- Forgetting to subtract the background count rate before finding half-life.
- Saying radioactive decay is affected by temperature or chemical reactions. It is not.
- Saying gamma radiation changes the nucleus into a new element. It does not change A or Z.
- Confusing ionising radiation with the radioactive source. Radiation does not make a person radioactive just by passing through them.
Exam tip: In half-life questions, first work out how many half-lives have passed, then halve step by step. Writing each stage makes arithmetic slips easy to spot.
Check yourself
- A GM tube reads 130 counts per minute near a source. The background is 20 counts per minute. What is the corrected count rate?
Answer
130 − 20 = 110 counts per minute. - A source has a count rate of 240 counts per second and a half-life of 12 minutes. What is the count rate after 36 minutes?
Answer
36 ÷ 12 = 3 half-lives. 240 → 120 → 60 → 30 counts per second. - (Extended) Americium-241 (proton number 95) emits an alpha particle. What are the nucleon number and proton number of the new nucleus?
Answer
Nucleon number 241 − 4 = 237. Proton number 95 − 2 = 93. - Why is a source with a short half-life used as a medical tracer in the body?
Answer
It stays active long enough to be detected, but its activity falls quickly, so the patient is exposed to radiation for a short time only.