Units, prefixes and standard form
Convert prefixes, squared and cubed units. Write numbers in standard form.
Radioactive decay and half-life questions
Calculate expected activity, subtract background and interpret half-life and natural-log gradients.
Practise
Decay constantA radionuclide has half-life 40 s. Calculate its decay constant. Give your answer to 3 significant figures.
Treat the given values as exact unless an uncertainty is stated.
Hint
Use λ = ln(2)/T½. Use natural logarithms.
Worked solution
- λ = ln(2)/40 s⁻¹.
- Answer: 0.0173 s⁻¹ (3 significant figures).
Question type: Mixed practice
Report a problem
Half-life describes a population
A particular nucleus decays randomly. For one radionuclide in unchanged conditions its decay probability per unit time is constant. The exponential model describes expected behaviour of many nuclei; measurements fluctuate.
Use seconds for activity
N = N₀ exp(−λt), A = λN and T½ = ln(2)/λ. Activity in Bq means expected decays per second, so λ must be in s⁻¹ when using A = λN. After n half-lives, expected activity is A₀/2ⁿ.
Correct count rates before finding a half-life
Subtract the background from both initial and later total count rates. Detector count rate is not automatically source activity: efficiency and geometry matter. The data exercises use idealised mean rates, fixed geometry and efficiency, and no contribution from daughter emissions.
Read a log-line gradient
ln(A/A₀) = −λt gives a straight line of gradient −λ. A base-10 logarithm has a different gradient. These questions use natural logarithms of a dimensionless ratio.
What this practice covers
Selected activity, half-life, background correction, log-line and random-decay tasks. Nuclear equations, binding energy, decay chains, safety procedures and dating models are outside this set.
A-level relevance
AQA 7408: 3.8.1.3 (selected); OCR A H556: 6.4.3 (selected). Tasks cover the selected skills listed above.