Radioactive decay and half-lifeEdexcel International A Level Physics: Subtopic test

1. 1
   A student sets up a Geiger–Müller tube and counter close to a long-lived source, whose half-life is many years, so its activity is effectively constant during the experiment. She records the number of counts in each of five successive 10 s intervals: 52, 47, 58, 44 and 55.

   (a)

   Which statement correctly describes nuclear decay as spontaneous?

   [1 mark]

   • AThe rate of decay increases as the temperature rises
   • BWhether a nucleus decays is not affected by external factors such as temperature, pressure or chemical state
   • CThe nuclei decay one after another in a fixed order
   • DA nucleus decays only when it is struck by another particle

   (b)

   Which statement correctly describes nuclear decay as random?

   [1 mark]

   • AEach nucleus decays after exactly one half-life
   • BAll the nuclei decay during the first half-life
   • CIt cannot be predicted when a particular nucleus will decay, but each has a constant probability of decaying per unit time
   • DNuclei decay in the order of their positions in the sample

   (c)

   Explain why the counts in the five intervals are different even though the activity of the source is constant.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Iodine-131 is a radioactive isotope with a half-life of 8.0 days. A hospital stores a sample of iodine-131 whose activity is 640 kBq. Use 1 day = 86 400 s.

   (a)

   What is the decay constant of iodine-131?

   [1 mark]

   • A1.00 × 10⁻⁶ s⁻¹
   • B8.66 × 10⁻² s⁻¹
   • C1.45 × 10⁻⁶ s⁻¹
   • D6.91 × 10⁵ s⁻¹

   (b)

   What is the activity of the sample after 24 days?

   [1 mark]

   • A213 kBq
   • B160 kBq
   • C0 kBq
   • D80 kBq

   (c)

   Calculate the number of undecayed iodine-131 nuclei in the sample when its activity is 640 kBq.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student measures the corrected activity of a sample of a radioactive isotope at regular intervals and obtains the following values: 480 Bq at 0 s, 340 Bq at 40 s, 240 Bq at 80 s, 170 Bq at 120 s and 120 Bq at 160 s.

   (a)

   Determine the half-life of the isotope from these results.

   [3 marks]

   (b)

   The student plots a graph of the natural logarithm of the activity, ln A, against time t. State the equation that predicts the shape of this graph, describe the graph, and use the data at 0 s and 160 s to find the decay constant.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Technetium-99m is a gamma-emitting isotope with a half-life of 6.0 hours that is used for medical imaging. A hospital receives a sample with an initial activity of 1200 MBq. In the equation N = N₀e^(−λt), N is the number of undecayed nuclei at time t, N₀ is the initial number and λ is the decay constant.

   (a)

   Calculate the activity of the sample 15 hours after it is received, and the time it takes for the activity to fall to 30 MBq.

   [6 marks]

   (b)

   Show that the decay constant and the half-life are related by λ = ln 2 ÷ t½, and use the equations for random decay to explain why the half-life of a given isotope is the same whatever the size of the sample.

   [6 marks]

   Total for question 4: 12 marks

End of questions