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Radioactive decay and half-life questions

Calculate expected activity, subtract background and interpret half-life and natural-log gradients.

Practise

Activity remaining

A single radionuclide has initial activity 1200 Bq and half-life 20 s. Calculate its expected activity after 40 s. No daughter activity contributes. Give your answer to 3 significant figures.

Expected activity during decayThe supplied exponential model; individual measurements would fluctuate. Horizontal axis: Time / s, 0 to 80. Vertical axis: Activity / Bq, 0 to 1200. Exact values are also listed below the graph.02040608003006009001200Time / sActivity / Bq
Read the axes and units. The values are also available in the table below.
Larger graph
Expected activity during decayThe supplied exponential model; individual measurements would fluctuate. Horizontal axis: Time / s, 0 to 80. Vertical axis: Activity / Bq, 0 to 1200. Exact values are also listed below the graph.02040608003006009001200Time / sActivity / Bq

Treat the given values as exact unless an uncertainty is stated.

Use decimals or e notation, e.g. 4.2e-3. Enter the unit separately.

Hint

Find the number of half-lives elapsed; activity halves each time.

Worked solution
  1. Number of half-lives = 40/20 = 2.
  2. A = 1200/2^2 Bq.
  3. Answer: 300 Bq (3 significant figures).
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Question type: Mixed practice
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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.

AQA specification · OCR A specification

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