How do I find a half-life from data?

See what fraction remains, count the halvings n, then divide the total time by n.

How is activity related to half-life?

A shorter half-life means a higher activity for the same mass, as more nuclei decay each second.

S5 Physics Radioactivity, Paper 2: working backwards from decay data

2026-11-02

Tutor Prep Guide · Physics

Each half-life halves the amount, and the number of halvings can be recovered from the remaining fraction.

Focus　Write the remaining fraction as one half to the power n, then multiply n by the half-life.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 3 · Intermediate 4 · Challenge 2 · Error redo 1
Chapter	Chapter: S5 Physics: Radioactivity
Level	S4 to S5

02　Questions (10 items)

FoundationA sample of half-life 3 days starts at 96 g. How much remains after 9 days?
FoundationWhich of alpha, beta and gamma radiation carries a negative charge?
FoundationA source of half-life 4 hours has an activity of 600 Bq. Find the activity after 12 hours.
IntermediateIodine-131 has a half-life of 8 days. How much of a 40 g sample remains after 32 days?
IntermediateA 2 g sample falls to 0.25 g in 24 days. Find the half-life.
IntermediateDescribe gamma radiation.
IntermediateRadium-226 (mass number 226, atomic number 88) emits a beta particle. Give the mass number and atomic number of the new nucleus.
ChallengeA source falls from 800 Bq to 100 Bq in 30 minutes. Find the half-life.
ChallengeA bone sample has 25 percent of its original carbon-14. Given a half-life of 5 730 years, estimate its age.
Error redoCorrect the claim: the half-life grows over time, which is why the radiation weakens.

03　Answers and one-line notes

#	Answer	One-line note
1	12 g	Nine days is three half-lives, so 96/2^3 = 12 g.
2	Beta particles	Beta particles are fast electrons and carry negative charge; alpha is positive and gamma is neutral.
3	75 Bq	Twelve hours is three half-lives, so 600/2^3 = 75 Bq.
4	2.5 g	Thirty-two days is four half-lives, so 40/2^4 = 2.5 g.
5	8 days	Going from 2 g to 0.25 g takes three halvings, so 24/3 = 8 days.
6	High-frequency electromagnetic waves with no charge and the greatest penetrating power	Gamma is energy only, with no mass or charge, and needs thick lead or concrete to stop it.
7	Mass number 226 and atomic number 89	In beta decay a neutron becomes a proton, so the mass number is unchanged and the atomic number rises by one.
8	10 minutes	Four halvings of the activity take three steps, so 30/3 = 10 minutes.
9	11 460 years	Twenty-five percent means two half-lives, so 2*5730 = 11 460 years.
10	It should read: the half-life is constant; what falls is the activity, because fewer nuclei remain.	The half-life belongs to the nuclide and does not change with temperature, pressure or elapsed time.

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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