IGCSE Physics Half-Life Questions and Worked Solutions (5.2.4) | 0625

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IGCSE Physics 0625 · Topic 5.2.4

IGCSE Physics Half-Life Questions and Worked Solutions

50 topic-wise practice questions on Half-Life (Unit 5: Nuclear Physics), written to the Cambridge IGCSE Physics 0625 syllabus for 2026–2028, each with a step-by-step worked solution.

50 questions20 Core20 Extended10 Challenge136 marksTextbook §5.2 · pp. 260–274
Questions tagged Core are for all candidates (Papers 1 & 3). Questions tagged Extended are Supplement content (Papers 2 & 4). Questions 41–50 are harder Challenge questions. Try each question first, then tap Show solution to check your working.

Topic guide: Half-Life

Half-life is the time for half the nuclei of an isotope in a sample to decay. It is constant for each isotope and is used to predict activity. (Extended) The type of radiation and the half-life decide which isotope is used for each application.

Key formulas

fraction remaining = (½)ⁿn = number of half-lives = time ÷ half-lifeCore
activity after n half-lives = initial ÷ 2ⁿhalving repeatedlyCore

Prerequisite knowledge

  • Radioactive decay (5.2.3)
  • Reading graphs
  • Background correction (5.2.1, Extended)

Exam tips & common mistakes

  • Count half-lives step by step: 800 → 400 → 200 → 100
  • Read half-life from a graph between any value and half of it
  • Justify applications with BOTH radiation type and half-life

Key facts from the syllabus (5.2.4)

  • Half-life: the time taken for half the nuclei of an isotope in a sample to decay
  • Use tables and decay curves to find half-life (Core: no background)
  • Extended subtract background before finding half-life from data
  • Extended smoke alarms — alpha, long half-life
  • Extended irradiating food and sterilising equipment — gamma
  • Extended thickness monitoring — beta for paper/thin sheets, gamma for thick metal; long half-life
  • Extended diagnosis and cancer treatment — gamma; tracers have short half-lives

Textbook: §5.2 Radioactivity, pp. 260–274

1
Core[1 mark]

Define half-life.

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Method: Half nuclei decay.

The time taken for half the nuclei of an isotope in a sample to decay
2
Core[2 marks]

A source has half-life 6.0 hours and initial activity 800 Bq. Calculate the activity after 18 hours.

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Method: 3 half-lives.

A = 800 ÷ 2³ = 100 Bq
3
Core[2 marks]

A sample has 1600 undecayed nuclei. Its half-life is 2 days. Calculate the number left after 8 days.

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Method: 4 half-lives.

N = 1600 ÷ 16 = 100
4
Core[2 marks]

An activity falls from 640 Bq to 80 Bq in 24 minutes. Calculate the half-life.

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Method: 3 half-lives.

640 → 320 → 160 → 80; t½ = 24 ÷ 3 = 8.00 min
5
Core[2 marks]

State the fraction of a sample remaining after 4 half-lives.

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Method: (½)⁴.

1/16
6
Core[2 marks]

A sample of 120 g of a radioisotope with half-life 5 years decays for 15 years. Calculate the mass remaining undecayed.

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Method: 3 half-lives.

m = 120 ÷ 8 = 15.0 g
7
Core[3 marks]

Count rate (corrected) values: 0 min: 200, 5 min: 140, 10 min: 100, 15 min: 70, 20 min: 50. Find the half-life.

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Method: 200 → 100 in 10 min.

10 minutes
8
Core[2 marks]

A source has half-life 12 s. Calculate how long until its activity drops to 1/8 of the initial value.

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Method: 3 half-lives.

t = 3 × 12 = 36 s
9
Core[3 marks]

A sample's activity is 2400 Bq. After 30 days it is 300 Bq. Calculate the half-life.

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Method: 3 half-lives.

t½ = 30 ÷ 3 = 10.0 days
10
Core[3 marks]

A radioisotope has half-life 8 days. A hospital receives 160 MBq. Calculate the activity after 32 days.

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Method: 4 half-lives.

A = 160 ÷ 16 = 10.0 MBq
11
Core[2 marks]

A source has activity 1200 Bq and half-life 3 days. Calculate the activity after 9 days.

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Method: 3 half-lives.

150 Bq
12
Core[2 marks]

State the fraction of nuclei remaining after 3 half-lives.

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Method: (½)³.

1/8
13
Core[2 marks]

State the fraction of nuclei that have decayed after 2 half-lives.

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Method: 1 − 1/4.

3/4
14
Core[3 marks]

A sample's activity falls from 2000 Bq to 125 Bq in 20 hours. Calculate the half-life.

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Method: 4 half-lives.

t½ = 20 ÷ 4 = 5.00 hours
15
Core[2 marks]

An isotope has a half-life of 5730 years. Calculate how long until 1/4 remains.

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Method: 2 half-lives.

11460 years
16
Core[3 marks]

Data: 0 s: 480 Bq; 30 s: 240 Bq; 60 s: 120 Bq. Determine the half-life and predict the activity at 120 s.

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Method: Halves every 30 s.

t½ = 30 s; at 120 s, 30 Bq
17
Core[2 marks]

Describe how to find half-life from a decay curve.

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Method: Read off times.

Read the time for the activity to fall from any value to half that value (repeat and average)
18
Core[3 marks]

A 64 mg sample has a half-life of 2.0 minutes. Calculate the mass remaining after 10 minutes.

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Method: 5 half-lives.

64 ÷ 32 = 2.00 mg
19
Core[2 marks]

Explain why the half-life of an isotope is constant.

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Method: Random, fixed probability.

Each nucleus has a fixed chance of decaying per unit time, so half always decay in the same time
20
Core[3 marks]

A source of activity 3200 Bq has a half-life of 15 minutes. Calculate the time for its activity to fall to 200 Bq.

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Method: 4 half-lives.

60 minutes
21
Extended[3 marks]

A measured count rate falls from 520 to 145 counts/min in 30 min. Background is 20 counts/min. Find the half-life.

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Method: Correct: 500 → 125 (2 half-lives).

Corrected: 500 → 125, two half-lives, so t½ = 15 min
22
Extended[3 marks]

Measured counts: 330 counts/min at t = 0, 180 at 4 h. Background is 30 counts/min. Find the half-life.

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Method: Correct: 300 → 150.

Corrected 300 → 150 in 4 h, so t½ = 4 h
23
Extended[2 marks]

Explain why an alpha emitter with a long half-life is used in smoke alarms.

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Method: Ionises air; lasts years.

Alpha ionises the air in the alarm but is easily stopped by smoke; a long half-life means it lasts for years
24
Extended[2 marks]

Explain why gamma radiation is used to sterilise medical equipment.

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Method: Penetrating.

It penetrates packaging to kill bacteria without the equipment needing to be opened
25
Extended[2 marks]

Explain why food can be irradiated with gamma rays to kill bacteria.

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Method: Penetrates, does not make food radioactive.

Gamma rays penetrate the food and kill bacteria; the food does not become radioactive
26
Extended[3 marks]

Explain why beta radiation is used to monitor the thickness of paper.

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Method: Partly absorbed.

Beta is partly absorbed by paper; small thickness changes cause a measurable change in count rate (alpha would be stopped, gamma would pass straight through)
27
Extended[2 marks]

Explain the choice of a long half-life source for thickness monitoring.

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Method: Steady count.

So the count rate does not fall noticeably due to decay, only due to thickness changes
28
Extended[3 marks]

Explain why a gamma emitter with a half-life of a few hours is used as a medical tracer.

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Method: Penetrates; short exposure.

Gamma passes out of the body to be detected and is weakly ionising; a short half-life means it does not stay radioactive in the body for long
29
Extended[2 marks]

Explain why gamma rays are used to treat cancer.

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Method: Kill cells.

Focused gamma rays penetrate to the tumour and kill the cancer cells
30
Extended[2 marks]

Explain why aluminium sheet thickness is monitored using gamma or beta rather than alpha.

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Method: Alpha stopped.

Alpha would be completely stopped by the metal, so no change could be measured
31
Extended[3 marks]

Measured counts (including 40 counts/min background): 0 min 840, 6 min 440, 12 min 240. Find the half-life.

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Method: Corrected: 800, 400, 200.

6 minutes
32
Extended[3 marks]

Measured activity is 1625 counts/min at t = 0 and 425 counts/min at t = 10 h. Background is 25 counts/min. Find the half-life.

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Method: Corrected 1600 → 400.

Two half-lives in 10 h, so t½ = 5 h
33
Extended[2 marks]

Explain why a source used for food irradiation has a long half-life.

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Method: Long use.

So it remains strong enough for a long time without frequent replacement
34
Extended[3 marks]

An alpha source in a smoke alarm has a half-life of 432 years. Explain why the alarm does not need its source replaced during its lifetime.

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Method: Long half-life.

Over a 10-year alarm life its activity hardly falls, so it keeps ionising the air at a nearly constant rate
35
Extended[2 marks]

State the type of radiation used to measure thickness of thin paper.

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Method: Beta.

Beta
36
Extended[2 marks]

State the type of radiation used to sterilise packaged syringes.

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Method: Gamma.

Gamma
37
Extended[3 marks]

Explain why a medical tracer should have a half-life of a few hours, not seconds or years.

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Method: Balance.

Long enough to be detected during the test, short enough that the patient is not exposed for long
38
Extended[3 marks]

Explain why beta (not gamma) is used to control the thickness of aluminium foil.

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Method: Partly absorbed.

Beta is partly absorbed by thin foil, so its count changes noticeably with thickness; gamma would pass through almost unchanged
39
Extended[2 marks]

State why an alpha emitter is not used as a medical tracer inside the body.

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Method: Highly ionising, not detected.

It would be absorbed in the body causing damage, and would not be detected outside
40
Extended[2 marks]

State why technetium-99m (gamma, half-life 6 h) is a good medical tracer.

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Method: Gamma and short half-life.

It emits gamma, which can be detected outside the body, and its short half-life limits the dose

Challenge questions

Harder, multi-step questions at the top end of the exam. Attempt these once you are confident with the questions above.

41
ChallengeCore[4 marks]

A sample contains 8.0 × 10¹² undecayed nuclei with half-life 3.0 h. Calculate the number left after 12 h and the number that have decayed.

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Method: 4 half-lives.

5.0 × 10¹¹ left; 7.5 × 10¹² decayed
42
ChallengeCore[4 marks]

A 1.6 MBq source has a half-life of 8.0 days. Calculate how many days it takes for the activity to fall below 0.10 MBq.

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Method: Halve repeatedly.

1.6 → 0.8 → 0.4 → 0.2 → 0.1: 4 half-lives = 32 days
43
ChallengeCore[4 marks]

Two sources A (t½ = 2 h, 800 Bq) and B (t½ = 4 h, 400 Bq) start together. Show that they have equal activity after 4 h.

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Method: Halve each.

A: 800 → 400 → 200; B: 400 → 200 — both 200 Bq after 4 h
44
ChallengeExtended[5 marks]

Measured (uncorrected) counts per minute: 0 h: 525; 2 h: 379; 4 h: 275; 6 h: 202; 8 h: 150. Background = 25 counts/min. Find the half-life.

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Method: Correct each reading by subtracting 25.

Corrected: 500, 354, 250, 177, 125 — halves from 500 to 250 in 4.0 h, and 250 to 125 in another 4.0 h: t½ = 4.0 h
45
ChallengeExtended[4 marks]

Explain why americium-241 (alpha, t½ = 432 years) is chosen for smoke alarms rather than a gamma source or a short half-life source.

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Method: Radiation type and t½.

Alpha strongly ionises the air and is blocked by smoke, and is stopped by the casing; gamma would pass through smoke and be hazardous; a long half-life keeps activity constant over the alarm's life
46
ChallengeExtended[4 marks]

A factory monitors thin plastic sheet thickness with a beta source above and a detector below. Explain how the system works and why a long half-life source is used.

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Method: Absorption and feedback.

Thicker sheet absorbs more beta, lowering the count; rollers are adjusted to keep it constant; a long half-life means changes are due to thickness, not decay
47
ChallengeExtended[4 marks]

Explain why a tracer for a medical scan should emit gamma, have a short half-life of a few hours and be chemically suitable.

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Method: Three criteria.

Gamma can be detected outside the body and is weakly ionising; a short half-life limits the dose; it must be absorbed by the organ studied
48
ChallengeExtended[4 marks]

Explain why gamma rays, not alpha or beta, are used to sterilise medical equipment, and why the equipment does not become radioactive.

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Method: Penetration.

Gamma penetrates packaging to kill bacteria; it does not make the nuclei of the equipment unstable, so it does not become radioactive
49
ChallengeExtended[4 marks]

Explain how gamma rays can treat a deep tumour while limiting damage to healthy tissue.

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Method: Multiple beams.

Beams from several directions are aimed to cross at the tumour, so it receives a large dose while surrounding tissue receives smaller doses
50
ChallengeExtended[4 marks]

A source has a half-life of 15 minutes. Its corrected count rate after 1.0 hour is 50 counts/min. Calculate the initial corrected count rate.

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Method: 4 half-lives back.

50 × 16 = 800 counts/min
All IGCSE Physics topics← 5.2.3 Radioactive Decay5.2.5 Safety Precautions →

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