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

1. 1
   A student counts the radiation from a long-lived radioactive source using a GM tube. She records the number of counts in each of ten successive 10-second intervals: 46, 53, 49, 55, 44, 51, 48, 52, 47 and 55. The activity of the source can be taken as constant throughout.

   (a)

   The counts in the intervals vary even though the activity is constant. What does it mean to say that radioactive decay is random?

   [1 mark]

   • AEvery nucleus decays after exactly one half-life
   • BThe decay rate depends on the temperature of the source
   • CIt is impossible to predict when an individual nucleus will decay
   • DThe decay rate is the same whatever the number of nuclei present

   (b)

   Radioactive decay is also spontaneous. What does this mean?

   [1 mark]

   • AA nucleus only decays after being hit by a neutron
   • BThe decay is not affected by external conditions such as temperature or pressure
   • CThe nuclei decay only when the source is heated
   • DThe decay can be speeded up by increasing the pressure

   (c)

   Explain why the counts differ from one interval to the next, and state what the student should do to make the count rate more precise.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A sample of an iodine isotope contains $2.4 \times 10^{15}$ undecayed nuclei at a particular time. The half-life of the isotope is 8.0 days. Take 1 day = 86 400 s.

   (a)

   What is the decay constant of this isotope?

   [1 mark]

   • A$1.4 \times 10^{-6}$ s⁻¹
   • B$8.7 \times 10^{-2}$ s⁻¹
   • C$1.0 \times 10^{6}$ s⁻¹
   • D$1.0 \times 10^{-6}$ s⁻¹

   (b)

   What is the activity of the sample at this time?

   [1 mark]

   • A$2.4 \times 10^{9}$ Bq
   • B$3.5 \times 10^{9}$ Bq
   • C$2.4 \times 10^{21}$ Bq
   • D$2.4 \times 10^{15}$ Bq

   (c)

   Calculate the activity of the sample 24 days later.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Technetium-99m is used as a radioactive tracer in hospitals. A sample of it has an activity of 400 MBq at 09:00, and its half-life is 6.0 hours. A scan needs the activity of the sample to have fallen to 60 MBq.

   (a)

   Calculate the decay constant of technetium-99m in s⁻¹.

   [3 marks]

   (b)

   Calculate how many hours after 09:00 the activity will have fallen to 60 MBq.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student measures the corrected count rate from a radioactive sample every 10 minutes. The corrected count rates, in counts per minute, at times of 0, 10, 20, 30, 40 and 50 minutes are 800, 570, 400, 280, 200 and 140. The natural logarithms of these count rates are 6.68, 6.35, 5.99, 5.63, 5.30 and 4.94.

   (a)

   Use the count rates to show that the half-life is 20 minutes, then calculate the decay constant in s⁻¹ and predict the corrected count rate after 90 minutes.

   [6 marks]

   (b)

   The student plots a graph of ln(corrected count rate) against time. Explain why this graph is a straight line, use the data to find the half-life, and evaluate the reliability of the readings at later times.

   [6 marks]

   Total for question 4: 12 marks

End of questions