Example 1
A sample has initial activity 800 Bq and half-life 3.0h. Find activity after 9.0h.
39=3 half-lives. A=800×(½)3=100 Bq.
Year 11 · SACE Stage 1
Half-life and activity calculations
Read exponential decay and subtract background count rates.
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Method and worked examples
Radioactive decay is random for an individual nucleus, but a large sample has a predictable exponential trend. After n half-lives, the undecayed fraction is (½)n. Activity is decays per second, measured in becquerels Bq, and follows the same fraction for one isotope with constant decay probability. Half-life does not depend on the sample’s initial size or ordinary chemical and physical state.
Use equal fractional decreases, not equal absolute decreases. Read the time for a net activity to halve on a decay graph, subtracting background first when using count rates. A detector’s count rate is not automatically the source activity because it detects only some emissions. These simple questions assume constant detector efficiency and geometry, and no additional radioactive components unless stated.
Example 1
Example 2
A detector reads 120 counts/min initially and 70 counts/min later. Background is 20 counts/min. What net-activity fraction remains?
Net initial rate =100 counts/min; net later rate =50 counts/min. Fraction =10050=21, so one half-life has elapsed under constant geometry.
Watch out: It loses the same fraction, one half of those still undecayed, so the absolute number lost decreases.