How do I count half-lives?

Divide the elapsed time by the half-life to get n, then the amount left is the original divided by two to the n.

How is a nuclear equation balanced?

Mass number must match on both sides first, then atomic number, which fixes the unknown particle.

S5 Physics Radioactivity, Paper 3: half-life and decay equations

2026-11-02

Works half-life forwards and backwards, alpha and beta changes, activity decay and fission balancing in ten graded items.

Focus　Count the number of half-lives first, then balance mass number before atomic number in every nuclear equation.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: S5 Physics: Radioactivity and Nuclear Decay
Level	Four basic, three advanced, two challenge and one error-repair item

02　Questions (10 items)

FoundationA nuclide has a half-life of 5 days. How much of 20 g remains after 15 days?
FoundationCarbon fourteen has a half-life of 5730 years. How old is a sample whose activity has fallen to 25 per cent?
FoundationRadium 226, mass number 226 and atomic number 88, emits one alpha particle. Find the mass and atomic numbers of the new nucleus.
FoundationCarbon fourteen, atomic number 6, emits one beta minus particle. Find the atomic number of the new nucleus.
IntermediateA sample of 64 g with a half-life of 8 days falls to 4 g. How long does that take?
IntermediateA source of 800 Bq decays for three half-lives. Find its activity.
IntermediateA 240 g sample falls to 30 g. If the half-life is 4 hours, how much time has passed?
ChallengeA source starts at 5.0 times ten to the six Bq with a half-life of 10 minutes. Find its activity after 40 minutes.
ChallengeIn the fission equation uranium 235 plus a neutron gives barium 141 plus krypton 92 plus x neutrons, what is x?
Error redoA student thinks two half-lives means everything has decayed and answers 0 g for a 96 g sample after 12 hours with a 6 hour half-life. What actually remains?

03　Answers and one-line notes

#	Answer	One-line note
1	2.5 g	Fifteen days is three half-lives, so twenty grams halves three times to 2.5 g.
2	11460 years	Twenty five per cent is two half-lives, so 5730 times 2 gives 11460 years.
3	222 and 86	An alpha particle removes four from the mass number and two from the atomic number, giving 222 and 86.
4	7, which is nitrogen	In beta minus decay a neutron turns into a proton, so the atomic number rises by one to 7.
5	32 days	Sixty four grams falling to four is sixteen fold, four half-lives, so 32 days.
6	100 Bq	Three half-lives divide the activity by eight, giving 100 Bq.
7	12 hours	Two hundred and forty grams falling to thirty is three half-lives, so 12 hours.
8	3.1 times ten to the five Bq	Forty minutes is four half-lives, so the activity falls to 312500 Bq, about 3.1 times ten to the five.
9	3	Mass number is conserved, so 141 plus 92 plus x must equal 236, giving three neutrons.
10	24 g	Half-life only halves the amount, so two half-lives leave a quarter, that is 24 g.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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