Knowledge Organiser: Half-Life
Key Terms
- Half-life: Time for activity to halve
- Activity: Decays per second (Bq)
- Becquerel (Bq): 1 decay per second
- Count rate: Detections per unit time
Key Facts
- Half-life is constant for each isotope
- Decay is random but statistically predictable
- Decay curve is exponential — never reaches 0
- Unaffected by temperature or pressure
Calculation Method
- Start → ÷2 → ÷2 → ÷2...
- Count halvings = number of half-lives
- n half-lives: activity × (½)ⁿ
- From graph: draw construction lines
Applications by Half-Life
- Medical tracers: hours
- Smoke detectors: years
- Carbon dating: 5,730 years
- Long half-life = long-term hazard
Key Equations
- After n half-lives: remaining amount = initial × (½)ⁿ
- Activity (Bq) = number of decays per second
- Activity halves every half-life (same as count rate)
- Carbon-14 half-life = 5,730 years (used in carbon dating)
Common Mistakes
- Thinking the sample completely decays after a few half-lives: After each half-life, the activity halves — it never reaches exactly zero; the sample approaches (but never reaches) zero activity
- Confusing activity and count rate: Activity is decays per second (Bq) measured at the source; count rate is what a detector measures — count rate is always less than activity due to detector efficiency and distance
- Applying the wrong half-life for an application: Medical tracers need short half-lives (hours) to minimise patient dose; carbon dating uses 5,730 years; smoke detectors use americium-241 (~430 years)
- Reading the half-life incorrectly from a graph: Find the time for activity to halve (not to reach zero) — locate one point, halve the y-value, then read across to the x-axis to find the half-life
- Forgetting background radiation in practical measurements: Always subtract background count rate from measured count rate before using the data to determine half-life
Memory Aid
- Half-life calculation method: Use the "halving chain" — write out each step:
- Start → ÷2 → ÷2 → ÷2 → ...
- Count how many times you had to divide to get to your answer. That's how many half-lives have passed.
- Remembering activity unit: "BecQuerel = Becquerel's Quantity per second" — he discovered radioactivity, so the unit is named after him. 1 Bq = 1 decay/second.
- Graph reading tip: Always draw your horizontal and vertical construction lines on graph questions — examiners look for this evidence of method and award marks for it even if you misread the value slightly.