Atomic and nuclear physics

Which statement about radioactive decay is correct?

1. A

   The exact decay time of each nucleus can be predicted

2. B

   Heating a sample makes every nucleus decay immediately

3. C

   Individual decays are random, but a large sample has a predictable statistical pattern

4. D

   A detector records every decay with no background counts

1. a

   Select and explain Select the correct statement and explain what ‘random’ means in this context.

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   Correct choiceC

   1. 1

      Selects option C: individual nuclear decays are random, while a large sample follows a predictable statistical pattern.

   2. 2

      Explains that the time at which one particular unstable nucleus decays cannot be predicted.

   3. 3

      Explains that probabilities allow the behaviour of many nuclei, such as half-life, to be predicted.

A detector records a background count rate of 20 counts per minute. The table shows the measured rate from a source plus background.

1. a

   Calculate Calculate the corrected source count rate at 0, 10, and 20 minutes.

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   1. 1

      Calculates 420 − 20 = 400 counts min⁻¹ at 0 min.

   2. 2

      Calculates 120 − 20 = 100 counts min⁻¹ at 10 min.

   3. 3

      Calculates 45 − 20 = 25 counts min⁻¹ at 20 min.

2. b

   Determine Determine the half-life and support it with two intervals.

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   1. 1

      Determines a half-life of 5 min.

   2. 2

      Supports it with two corrected halvings, for example 400 → 200 → 100 over successive 5 min intervals.

3. c

   Predict Predict the measured detector rate at 25 minutes.

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   1. 1

      Halves the corrected 20 min rate from 25 to 12.5 counts min⁻¹.

   2. 2

      Adds background to predict about 32.5 counts min⁻¹, accepting 32 or 33 for a whole-count-rate estimate.

A hospital needs a tracer that can be detected outside the body during a scan completed within two hours. Consider the simplified candidates below.

1. a

   Select Select the most suitable isotope and justify your choice using two properties.

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   1. 1

      Selects isotope P as the most suitable tracer for the two-hour diagnostic scan.

   2. 2

      Explains that gamma radiation can leave the body and be detected externally.

   3. 3

      Explains that 6 h is long enough for preparation and scanning but much shorter than 8 d, reducing prolonged exposure and waste activity.

2. b

   Explain Explain why isotope R is unsuitable even though its half-life is short.

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   1. 1

      Alpha radiation is poorly penetrating and is unlikely to escape the body for external imaging.

   2. 2

      Its 3 min half-life may be too short for transport, preparation, administration, and the scan.

3. c

   Evaluate Evaluate two practical controls that should accompany the use of isotope P.

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   1. 1

      Identifies a valid control such as minimising activity and time, maximising distance, shielding, secure handling, monitoring, or planned waste storage.

   2. 2

      Explains how one named control reduces dose or prevents contamination.

   3. 3

      Explains a second control or links decisions to patient benefit, staff exposure, and responsible waste management.