Half-life, irradiation and contamination – GCSE Physics exam questions with mark scheme

1Grade 4–53 marks

The graph shows how the activity of a radioactive sample changes with time.

(a) Use the graph to determine the half-life of the sample. Show on the graph how you got your answer. [2]

(b) Determine the activity of the sample after 12 hours. [1]

(a) reading of half the initial activity (400 Bq) taken from graph / shown on graph(1)
(a) 4 hours (allow 3.8–4.2 h)(1)
(b) 100 Bq (allow 90–110 Bq)(1)
Answer: (a) 4 hours (b) 100 Bq
Examiner tip: Read the time for the activity to fall from 800 to 400 Bq — always halve the starting value, not the axis maximum.

2Grade 6–7Higher4 marks

A sample of iodine-131 has a half-life of 8 days. The initial activity of the sample is 2400 Bq.

(a) Calculate the activity of the sample after 24 days. [2]

(b) Calculate the net decline in activity after 24 days, expressed as a fraction of the initial activity. Give your answer in its simplest form. [2]

(a) 24 ÷ 8 = 3 half-lives or 2400 → 1200 → 600 shown(1)
(a) 300 (Bq) an answer of 300 Bq scores 2 marks(1)
(b) net decline = 2400 − 300 = 2100 (Bq) or fraction remaining = $\tfrac{1}{8}$ so decline = $1 - \tfrac{1}{8}$ allow ecf from (a)(1)
(b) $\dfrac{7}{8}$ (allow 0.875 / 7 : 8 / 87.5%) do not accept $\tfrac{1}{8}$ (that is the fraction remaining) an answer of 7/8 scores 2 marks(1)
Answer: (a) 300 Bq (b) $\dfrac{7}{8}$
Examiner tip: Net decline is how much the activity has DROPPED by, not the activity that is left.

3Grade 6–74 marks

A technician moves a radioactive source using long-handled tongs.

(a) Explain the difference between irradiation and radioactive contamination. [2]

(b) Explain why a source that emits alpha particles is more dangerous inside the body than outside the body. [2]

(a) irradiation: exposure to radiation from a source outside the object (the object does not become radioactive) allow irradiation stops when the source is removed(1)
(a) contamination: unwanted presence of radioactive atoms on or in a material/person allow radioactive material/source gets onto or into the object/person (so it keeps being exposed / becomes radioactive)(1)
(b) outside the body alpha is absorbed by the air / skin, so cannot reach living cells (allow alpha has a short range / is not very penetrating)(1)
(b) inside the body alpha is highly ionising, so it damages nearby cells / DNA allow inside the body all the alpha radiation is absorbed by (nearby) living cells/tissue(1)
Answer: Irradiation is exposure to radiation from outside; contamination is radioactive material getting on or into something. Alpha is stopped by skin but is very strongly ionising inside the body.
Examiner tip: Do not say an irradiated object 'becomes radioactive' — that is contamination.

4Grade 1–3Foundation3 marks

A teacher describes a sample of a radioactive isotope to a class.

(a) Complete the sentence.

The half-life of a radioactive isotope is the time it takes for the number of ____________ in a sample of the isotope to halve. [1]

(b) Radioactive decay is a random process.

Which statement describes what this means? Tick (✓) one box. [1]

☐ All of the nuclei in the sample decay at the same time.
☐ It is not possible to predict which nucleus will decay next.
☐ The nuclei decay faster when the sample is heated.
☐ Each nucleus decays after exactly one half-life.

What fraction of the original unstable nuclei will still be undecayed after 5 minutes? [1]

(a) (unstable / undecayed / radioactive) nuclei; allow atoms (of the isotope); do not accept particles / neutrons / electrons(1)
(b) It is not possible to predict which nucleus will decay next (second box only); more than one box ticked = 0(1)
(c) $\frac{1}{2}$; allow half / 0.5 / 50%(1)
Answer: (a) unstable nuclei (b) It is not possible to predict which nucleus will decay next. (c) $\frac{1}{2}$
Examiner tip: In (a) the word must be nuclei (or atoms) – 'particles' is too vague and does not score.

5Grade 4–5Triple only3 marks

A student uses a Geiger–Muller tube and counter to measure the count rate from a radioactive source.

Before the source is brought near, the student measures the background count rate. It is 20 counts per minute.

The table shows the student's results with the source in place.

Time in minutes	0	1	2	3	4	5	6
Measured count rate in counts per minute	660	473	340	246	180	133	100

(a) Give one source of background radiation. [1]

(b) Determine the half-life of the source. Show how you work out your answer. [2]

(a) any one from: rocks / soil / radon gas (from rocks) / cosmic rays (from space) / fallout from nuclear weapons testing / nuclear accidents (eg Chernobyl, Fukushima); allow medical X-rays / building materials; ignore 'the Sun' on its own; ignore 'the air' unless radon is named(1)
(b) background count subtracted from readings: eg 660 − 20 = 640 (counts/min) and half of 640 = 320, which corresponds to a measured reading of 340 (counts/min); allow any correct halving pair after correction, eg 340 − 20 = 320 → 160 + 20 = 180(1)
(b) half-life = 2 (minutes); an answer of 2 minutes with no working scores 1 mark only; an answer of about 2.1 minutes from halving 660 to 330 without subtracting background scores 0(1)
Answer: (a) eg radon gas from rocks / cosmic rays (b) 2 minutes
Examiner tip: Subtract the background count from every reading before you halve – halving 660 to 330 gives the wrong half-life.

6Grade 4–53 marks

A hospital receives a sample of a radioactive isotope used to examine a patient's thyroid.

When the sample arrives, its activity is 1200 Bq.

36 hours later, the activity of the sample is 75 Bq.

Calculate the half-life of the isotope. Show your working. [3]

successive halvings shown: 1200 → 600 → 300 → 150 → 75 (Bq); allow $\frac{1200}{75} = 16$ or $\frac{75}{1200}=\frac{1}{16}$(1)
number of half-lives = 4(1)
half-life = 36 ÷ 4 = 9 hours; correct answer with no working scores 3 marks; unit required for 3rd mark; an answer of 2.25 h (36 ÷ 16) scores 1 mark(1)
Answer: 9 hours
Examiner tip: Count the number of halvings (4), not the factor the activity falls by (16): 36 ÷ 16 is a common wrong answer.

7Grade 8–9Higher5 marks

Caesium-137 is a radioactive isotope released into the environment by a nuclear accident. It has a half-life of 30 years.

(a) Calculate the ratio

$$\text{number of undecayed caesium-137 nuclei after 150 years} : \text{number of caesium-137 nuclei originally released}$$

Give your answer in the form 1 : $n$. [2]

(b) At a certain time after the accident, the ratio

$$\text{number of nuclei that have decayed} : \text{number of nuclei still undecayed}$$

is 15 : 1.

Calculate how many years after the accident this happens. [3]

(a) 150 ÷ 30 = 5 half-lives(1)
(a) 1 : 32; allow 1 : 2⁵(1)
(b) fraction still undecayed = $\frac{1}{16}$ (of the original); allow 1 out of every 16 nuclei is undecayed(1)
(b) $\frac{1}{16} = \left(\frac{1}{2}\right)^4$ so 4 half-lives; allow 1 → ½ → ¼ → ⅛ → $\frac{1}{16}$ shown(1)
(b) 4 × 30 = 120 years; allow ecf from an incorrect number of half-lives × 30; an answer of 450 years (15 × 30) scores 0(1)
Answer: (a) 1 : 32 (b) 120 years
Examiner tip: In (b) 15 : 1 means 1 nucleus in every 16 is left, not 1 in 15 – work out the undecayed fraction first.

8Grade 6–75 marks

A student measures the count rate from a radioactive sample every 10 minutes. She subtracts the background count rate from each reading.

The graph shows her corrected results (×) and a line of best fit.

(a) Use the line of best fit to determine the half-life of the sample. Show on the graph how you work out your answer. [2]

(b) Predict the corrected count rate 2 hours after the start of the measurements. [2]

Give the reason for this. [1]

(a) lines drawn on the graph from any count rate on the curve and from half that count rate to the time axis, eg 640 → 320 or 400 → 200(1)
(a) half-life = 20 minutes; allow 19–21 minutes(1)
(b) 120 ÷ 20 = 6 half-lives; allow ecf from (a)(1)
(b) 640 ÷ 2⁶ = 10 counts per minute; allow ecf from (a); allow 9–11(1)
(c) radioactive decay is random; allow you cannot predict when a nucleus will decay; ignore 'errors in reading' / 'human error'(1)
Answer: (a) 20 minutes (b) 10 counts per minute (c) radioactive decay is random
Examiner tip: In (b) 2 hours must be changed to 120 minutes first; then halve 640 six times rather than reading off the graph, which stops at 80 minutes.

9Grade 4–54 marks

Some fruit is exposed to gamma radiation from a sealed radioactive source. This kills bacteria and makes the fruit last longer before going bad.

(a) A shopper is worried that the fruit has become radioactive.

Explain why the fruit does not become radioactive. [2]

(b) Scientists study the effects of radiation on the human body. They publish their results so that other scientists can peer-review them.

Explain why it is important that the results are peer-reviewed. [2]

(a) the fruit is irradiated / only exposed to radiation (from outside); allow the radiation passes through the fruit(1)
(a) no radioactive material / source gets onto or into the fruit; allow the fruit is not contaminated; allow the source is sealed so it does not touch the fruit(1)
(b) other scientists check the method / data / conclusions; allow other scientists repeat the experiments (to see if they get the same results)(1)
(b) so that errors or bias can be found / so that the findings can be shown to be valid; allow so that the findings are trusted / accepted (by other scientists) before decisions about safety are made(1)
Answer: (a) The fruit is only irradiated: no radioactive material gets on or into it. (b) Other scientists check or repeat the work, so mistakes or bias are found and the findings can be trusted.
Examiner tip: Irradiation never makes an object radioactive – only contamination (radioactive atoms on or in the object) does.

10Grade 6–76 marks

A research laboratory uses two radioactive sources.

Source A is a sealed metal capsule containing an isotope that emits gamma radiation. It is stored in a lead-lined box.
Source B is a liquid containing an isotope that emits beta radiation. Its half-life is 14 days. Small volumes of the liquid are poured into test tubes during experiments.

Compare the hazards to the scientists from irradiation and from contamination when they use these two sources.

Describe the precautions the scientists should take with each source. [6]

Hazards – irradiation (mainly Source A): scientists are exposed to gamma radiation from outside the body; gamma is very penetrating so it can reach internal organs from a distance and pass through skin / clothing; the risk only lasts while the source is out of its box / near the person; once the source is put away or moved away the exposure stops; the scientist does not become radioactive(1)
Hazards – contamination (mainly Source B): the liquid could be spilled / splashed onto skin, clothing or benches, or swallowed / breathed in; radioactive atoms then stay on or in the body, so the person keeps being exposed even after leaving the lab; inside the body beta radiation is absorbed by and ionises nearby cells / tissue; damage to cells / DNA can lead to cancer or mutations(1)
Comparison / half-life: contamination is harder to remove and keeps irradiating until removed or decayed; with a 14-day half-life the activity takes weeks to fall significantly (eg to ⅛ after 42 days); irradiation from Source A can be stopped immediately by shielding or distance(1)
Precautions – Source A: keep it in the lead-lined box when not in use; handle it with long tongs / keep a large distance; use it for as short a time as possible; use lead / thick concrete shielding; never point it at people; wear a dosimeter / film badge to monitor dose(1)
Precautions – Source B: wear disposable gloves, a lab coat and eye protection; use drip trays / spill trays; do not eat or drink in the lab; wash hands afterwards; check hands, clothes and benches with a detector (Geiger–Muller tube) for contamination; label and dispose of waste / used test tubes as radioactive waste; store in a labelled, shielded, sealed container(1)

Level	Marks	What it looks like
Level 3	5–6	A clear, logically organised comparison of the hazards of irradiation and contamination applied to both sources, with precautions for each source that are linked to the hazard they reduce.
Level 2	3–4	Relevant hazards of both irradiation and contamination are described, with some precautions, but the comparison is limited or the precautions are not clearly linked to the right source.
Level 1	1–2	Simple statements about the danger of radiation or a few isolated precautions, with little or no distinction between irradiation and contamination.
No relevant content	0	Nothing worthy of credit.

Answer: Irradiation (Source A, gamma): external exposure that stops when the source is shielded or moved away – precautions: lead box, tongs, distance, short exposure time, dosimeter. Contamination (Source B, beta liquid): radioactive atoms on or in the body keep irradiating for weeks (14-day half-life) and beta is highly damaging inside the body – precautions: gloves, coat, spill trays, no eating, hand-washing, contamination monitoring, safe disposal.
Examiner tip: To reach Level 3 you must COMPARE the two hazards (eg contamination keeps going after you leave the lab; irradiation stops when the source is put away) – just listing precautions caps you at Level 2.

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