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Physics · Grades 9–12

Half-life: a statistical model

Apply repeated halving without predicting an individual decay time.

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Half-life

After one half-life the expected undecayed amount is half the initial amount in a large ensemble.

Repeated intervals

After n half-lives the expected fraction is (1/2) to the power n, not 1/(2n).

Random events

Individual nuclear decay times are random. Half-life describes population behaviour.

Safety scope

Use supplied numbers or simulations only. No radioactive-source handling activity is part of this material.

Worked examples

A model starts with 64000 undecayed nuclei. Find the expected number after three half-lives.

64000/2³ = 8000.

8000

A half-life is 6 h. How many half-lives pass in 24 h?

24/6 = 4 intervals.

4

Check your understanding

  1. Does half-life predict exactly when one particular nucleus decays?

    1. Yes, every nucleus decays at the half-life
    2. No
    3. Only if it is first in the list

  2. A model expected amount falls from 800 to 100 after repeated half-lives. How many half-lives occurred?

  3. Why is dividing the initial amount by six incorrect for three half-lives?

Answers and marking notes

Answers and marking notes
  1. No

    Individual decays are random; half-life is statistical.

  2. 3

    800 → 400 → 200 → 100 gives three halvings.

  3. Three repeated halvings divide by 2³ = 8, not 2 × 3 = 6.

    Credit exponential rather than linear halving.

Further reading and review references

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Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.