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.
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.
- 1Find the number of half-lives: n = 45 ÷ 15 = 3.
- 2Use A = A₀ ÷ 2ⁿ: A = 240 ÷ 2³.
- 3Work out 2³ = 8, so A = 240 ÷ 8.
- 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).
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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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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