Calculate a remaining amount after half-lives

Supplied materials

• Paper-only fictional isotope model: its half-life is 3 hours. Start with a modelled radioactive amount of 80 units. Do not obtain or handle radioactive material.
• Use N(t) = 80 × (1/2)^(t/3). For this task, the quantities describe modelled amounts, not an exact count of individual atoms.

Learn the idea

Half-life is the time interval over which a radioactive amount falls to half in the decay model. Repeating the same fractional reduction produces exponential decay, not subtraction of a fixed amount each hour.

Individual atoms decay probabilistically. A smooth model is useful for an amount or expected count, but a very small collection need not lose exactly half its atoms in each interval. Decay does not mean matter simply vanishes; nuclei transform.

1. Make a table for 0, 3, 6 and 9 hours.
2. Halve the preceding modelled amount at each 3-hour step.
3. Count elapsed half-life intervals before using the exponent.
4. Calculate the remaining amount at 12 hours.

Check your reasoning

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Take it further

If the half-life were 6 hours instead, 12 hours would contain only two half-lives and leave 20 units. Explain why both the elapsed time and half-life matter.

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