Radioactive dating compares the remaining parent isotope, its activity or accumulated daughter product with a justified starting condition. If a closed sample retains one quarter of its original parent amount, two half-lives have passed. Age equals number of half-lives times half-life. The method requires appropriate assumptions about initial composition, later contamination and loss or gain of relevant isotopes.
Activity and hazard are different quantities. Long half-life means activity declines slowly, but initial activity, radiation type, chemical form and containment also matter. A mixed waste sample may contain several isotopes and need separate decay calculations. For the simple comparisons here, use the supplied single-isotope model and stated target fraction. Do not turn a computed fraction into an unsupported declaration that material is safe.
Example 1
A closed sample has 12.5% of its original radioactive parent. Half-life is 6000y. Find model age.
12.5% =81=(21)3. Three half-lives have elapsed, giving age=3×6000=18000y.
Example 2
A single-isotope waste sample must fall from 800 Bq to 50 Bq. Half-life is 10y. Find the model time.
800→400→200→100→50 is four half-lives. Time =40y. This activity target is not by itself a safety criterion.
Watch out: The calculation depends on a justified initial value and a closed-system history; contamination or loss can invalidate that model.