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PhysicsGCSEAQA & EdexcelYears 10–11

GCSE Physics Radioactive Decay & Half-life Notes

Unstable nuclei decay by emitting radiation, changing the nucleus. Half-life lets you predict how the activity of a sample falls over time.

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Key concepts

Radioactive decay
The random emission of radiation from an unstable nucleus, which becomes more stable in the process.
Activity
The number of decays per second, measured in becquerels (Bq). Activity decreases over time as fewer unstable nuclei remain.
Decay equations
Alpha decay reduces the mass number by 4 and the atomic number by 2; beta decay leaves the mass number unchanged but increases the atomic number by 1.
  • A decay (or count-rate) curve halves in height every half-life.
  • Alpha decay: a nucleus loses 2 protons and 2 neutrons.
  • Beta decay: a neutron turns into a proton and a fast electron is emitted.

Key formulas

Activity after n half-lives

A = A₀ ÷ 2ⁿ

n = time ÷ half-life.

Worked example

A radioactive source has a count rate of 240 counts/min and a half-life of 15 minutes. Find the count rate after 45 minutes.

  1. 1Find the number of half-lives: n = 45 ÷ 15 = 3.
  2. 2Use A = A₀ ÷ 2ⁿ: A = 240 ÷ 2³.
  3. 3Work out 2³ = 8, so A = 240 ÷ 8.
  4. 4Calculate: A = 30 counts/min.

Answer: 30 counts/min

Common mistakes

✗ Multiplying instead of dividing by 2 each half-life.

✓ Activity halves each half-life — divide, not multiply.

✗ Getting the decay equation numbers wrong.

✓ Alpha: mass −4, atomic −2. Beta: mass unchanged, atomic +1.

✗ Forgetting to subtract background count rate.

✓ If a background reading is given, subtract it before finding half-life.

Quick check

Try these, then reveal the answers.

How does the atomic number change in beta decay?Reveal answer

It increases by 1.

A source drops from 320 Bq to 40 Bq in 12 hours. Find the half-life.Reveal answer

320→160→80→40 is 3 half-lives, so 12 ÷ 3 = 4 hours.

What does activity measure?Reveal answer

The number of nuclear decays per second (in becquerels).

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Exam tips

  • Read half-life off a graph by finding the time for the count rate to halve — check it halves again to confirm.
  • For decay equations, balance the mass numbers (top) and atomic numbers (bottom) on both sides.
  • Subtract background radiation before doing half-life calculations when it is given.

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Related topics

Atomic Structure & RadioactivityElectromagnetic Spectrum

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Frequently asked questions

How do you find half-life from a decay curve?+

Read the time taken for the count rate to fall to half its starting value; a good answer checks that it halves again over the next equal time interval.

What changes in the nucleus during alpha and beta decay?+

In alpha decay the nucleus loses 2 protons and 2 neutrons; in beta decay a neutron becomes a proton and a fast electron (the beta particle) is emitted.

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