4.4.2.1Radioactive decay and nuclear radiation
Some atomic nuclei are unstable. The nucleus gives out radiation as it changes to become more stable. This is a random process called radioactive decay.
Activity is the rate at which a source of unstable nuclei decays. Activity is measured in becquerel (Bq).
Count-rate is the number of decays recorded each second by a detector, such as a Geiger-Muller tube.
The two are not the same. Activity is what the source is actually doing; count-rate is what a detector happens to pick up, which is always less because the detector only catches radiation heading its way.
The nuclear radiation emitted may be:
• an alpha particle (α) — this consists of two neutrons and two protons; it is the same as a helium nucleus • a beta particle (β) — a high speed electron ejected from the nucleus as a neutron turns into a proton • a gamma ray (γ) — electromagnetic radiation from the nucleus • a neutron (n).
Required knowledge of the properties of alpha particles, beta particles and gamma rays is limited to their penetration through materials, their range in air, and ionising power — so nothing else about them is examinable.
You should be able to apply your knowledge to the uses of radiation and evaluate the best sources of radiation to use in a given situation.
That evaluation always comes back to the table above. A source used inside the body should not be strongly ionising and must be able to get out to a detector, so gamma is chosen. A source used to check the thickness of aluminium foil must be partly stopped by it, so beta is chosen — alpha would all be absorbed and gamma would all pass through, and in either case the reading would not change with thickness.
Worked example
A smoke detector uses a source whose radiation must ionise the air in a small gap but must not escape the plastic case. Which type should be used, and why?
- The radiation must ionise the air strongly, so that a current flows across the gap.
- Alpha is strongly ionising; beta and gamma are much less so.
- The radiation must not escape the case, for safety.
- Alpha has a range of only a few centimetres in air and is stopped by paper, so it cannot get out.
- Both requirements point the same way.
Answer: Alpha — it is strongly ionising, so it ionises the air in the gap, and its very short range in air means it cannot escape the detector.
- Radioactive decay
- the random process in which an unstable nucleus gives out radiation as it changes to become more stable
- Activity
- the rate at which a source of unstable nuclei decays, measured in becquerel (Bq)
- Count-rate
- the number of decays recorded each second by a detector such as a Geiger-Muller tube
4.4.2.2Nuclear equations
Nuclear equations are used to represent radioactive decay. In a nuclear equation an alpha particle is represented by the symbol ⁴₂He, and a beta particle by ⁰₋₁e.
The emission of the different types of nuclear radiation may cause a change in the mass and/or the charge of the nucleus.
• Alpha decay causes both the mass and the charge of the nucleus to decrease — the mass number falls by 4 and the atomic number by 2. • Beta decay does not cause the mass of the nucleus to change, but does cause the charge of the nucleus to increase — the mass number is unchanged and the atomic number rises by 1. • The emission of a gamma ray does not cause the mass or the charge of the nucleus to change.
Beta decay looks strange until you see where the electron comes from: a neutron in the nucleus turns into a proton, and the electron is ejected. The total number of particles in the nucleus is unchanged, which is why the mass number stays the same, but there is now one more proton, so the atomic number rises by one.
You should be able to use the names and symbols of common nuclei and particles to write balanced equations that show single alpha and beta decay. This is limited to balancing the atomic numbers and mass numbers — the identification of daughter elements from such decays is not required, so you will not have to name the new element. You are also not required to recall the two worked examples printed in the specification.
Worked example
Complete the alpha decay equation: ²²⁶₈₈Ra → ?? + ⁴₂He
- Balance the mass numbers, the top numbers: 226 = ? + 4, so the daughter has 222.
- Balance the atomic numbers, the bottom numbers: 88 = ? + 2, so the daughter has 86.
- Write the daughter with those numbers.
- You are not required to name the element, only to balance the numbers.
Answer: ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He — the mass number falls by 4 and the atomic number by 2, as alpha decay always does.
Worked example
Complete the beta decay equation: ¹⁴₆C → ?? + ⁰₋₁e
- Balance the mass numbers: 14 = ? + 0, so the daughter still has 14.
- Balance the atomic numbers: 6 = ? + (−1), so the daughter must have 7.
- The beta particle's atomic number is −1, which is why the daughter's goes up rather than down.
- Write the daughter with mass number 14 and atomic number 7.
Answer: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e — mass unchanged, charge increased by one.
Common mistake
The beta particle carries an atomic number of −1. Subtracting a negative means the daughter's atomic number increases — which is why beta decay moves an element up the periodic table while alpha moves it down.
4.4.2.3Half-lives and the random nature of radioactive decay
Radioactive decay is random.
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 time it takes for the count rate — or activity — from a sample containing the isotope to fall to half its initial level.
You should be able to explain the concept of half-life and how it is related to the random nature of radioactive decay.
The link between the two is the point of this section. It is impossible to say when any individual nucleus will decay — that is what random means. But a sample contains an enormous number of nuclei, and although each one is unpredictable, the proportion decaying in a given time is highly predictable. Half-life is a statement about that reliable average behaviour of a huge number, not a prediction about any one nucleus.
You should be able to determine the half-life of a radioactive isotope from given information — usually a table or a graph of count-rate against time. Find the initial value, halve it, and read off the time at which the curve reaches that level.
Worked example
A source has a count-rate of 800 counts per second. After 12 hours it has fallen to 100 counts per second. Calculate the half-life.
- Halve repeatedly from the starting value: 800 → 400 → 200 → 100.
- That took three halvings.
- Three half-lives occupy 12 hours.
- One half-life = 12 ÷ 3.
Answer: 4 hours
- Half-life
- the time it takes for the number of nuclei of a radioactive isotope in a sample to halve, or for the count rate from the sample to fall to half its initial level
4.4.2.3Net decline after several half-livesHigher tier
Higher tier students should be able to calculate the net decline, expressed as a ratio, in a radioactive emission after a given number of half-lives.
After n half-lives the fraction remaining is 1 ÷ 2ⁿ. The net decline expressed as a ratio compares what is left with what there was at the start.
Worked example
Calculate the net decline in the count-rate of a source after 4 half-lives, as a ratio.
- After each half-life the count-rate halves.
- After 4 half-lives the fraction remaining is 1 ÷ 2⁴.
- 2⁴ = 16, so one sixteenth remains.
- As a ratio of remaining to original, that is 1 : 16.
- Check by halving: 1 → ½ → ¼ → ⅛ → 1/16.
Answer: 1 : 16, or one sixteenth of the original count-rate remains.
Common mistake
Four half-lives does not mean the activity falls to zero, and it does not mean it falls by four halves. Each half-life halves what is left at that moment, so the decline is 1 ÷ 2ⁿ, never all the way to nothing.
4.4.2.4Radioactive contamination
Radioactive contamination is the unwanted presence of materials containing radioactive atoms on other materials. The hazard from contamination is due to the decay of the contaminating atoms. The type of radiation emitted affects the level of hazard.
Irradiation is the process of exposing an object to nuclear radiation. The irradiated object does not become radioactive.
That last sentence is the whole distinction, and it is examined constantly. Contamination means the radioactive material itself is on or in the object, so the hazard continues until it is removed. Irradiation means only the radiation reached the object; move the object away, or remove the source, and the exposure stops immediately.
You should be able to compare the hazards associated with contamination and irradiation. Alpha is the greatest hazard inside the body because it is strongly ionising and all its energy is deposited in a very short distance in nearby tissue. From outside the body it is the least hazardous, because it cannot even penetrate skin. Gamma is the reverse on both counts.
Suitable precautions must be taken to protect against any hazard that the radioactive source used in the process of irradiation may present — for example handling sources with tongs, storing them in lead-lined containers, keeping exposure times short, and standing well back.
You should also understand that it is important for the findings of studies into the effects of radiation on humans to be published and shared with other scientists, so that the findings can be checked by peer review. Peer review lets other scientists examine the method and the data before conclusions are accepted, which catches errors and bias — and on a subject as consequential as radiation exposure, that matters.
- Radioactive contamination
- the unwanted presence of materials containing radioactive atoms on other materials; the hazard comes from the decay of the contaminating atoms
- Irradiation
- the process of exposing an object to nuclear radiation; the irradiated object does not become radioactive
Before you practise
- Radioactive decay is random; activity is the rate of decay, measured in becquerel, and count-rate is what a detector records each second.
- Alpha is two protons and two neutrons — a helium nucleus; beta is a high speed electron ejected as a neutron turns into a proton; gamma is electromagnetic radiation from the nucleus; a neutron may also be emitted.
- Alpha: stopped by paper, few centimetres in air, strongly ionising. Beta: a few millimetres of aluminium, about a metre, moderately ionising. Gamma: thick lead, very long range, weakly ionising.
- Alpha decay reduces the mass number by 4 and the atomic number by 2; beta decay leaves the mass number unchanged and raises the atomic number by 1; gamma changes neither.
- Balance nuclear equations on mass number and atomic number only — naming the daughter element is not required.
- Half-life is the time for the number of nuclei, or the count-rate, to halve.
- Individual decays are unpredictable, but the proportion decaying in a given time is reliable because a sample contains so many nuclei.
- Higher tier: after n half-lives the fraction remaining is 1 ÷ 2ⁿ.
- Contamination is radioactive material on the object; irradiation is exposure to radiation, and the irradiated object does not become radioactive.