Radioactivity
5 marks · NormalA student investigates the decay of a radioactive isotope by measuring its activity (in Bq). The data below shows the measured activity at 10-minute intervals, after correcting for background radiation.
| Time (min) | Activity (Bq) |
|---|---|
| 0 | 480 |
| 10 | 240 |
| 20 | 120 |
| 30 | 60 |
Describe what is meant by the half-life of a radioactive isotope.
Use the table to determine the half-life of this isotope. Show your working.
Explain why the measured activity falls as time passes.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) Half-life is the average time taken for half the radioactive atoms in a sample to decay.
(b) Half-life is 10 minutes. Working: Activity halves every 10 minutes (480 → 240 → 120 → 60). minutes
(c) The activity falls because as the radioactive atoms decay, there are fewer undecayed nuclei left that can decay, so the rate of disintegration decreases over time. Decay is random, but the number of atoms available falls exponentially.
Show mark scheme and worked solution
Marking points
C1 (a) · 1 mark · States correct definition of half-life (average time for half of the radioactive atoms to decay).
C2 (b) · 1 mark · Identifies from the table that each 10-min interval halves the activity.
C3 (b) · 1 mark · States correct half-life: 10 minutes, with working shown.
C4 (c) · 1 mark · Explains activity falls because fewer undecayed nuclei remain as decays happen.
C5 (c) · 1 mark · Mentions that radioactive decay is random and the rate (activity) decreases over time (exponential decay).
Worked solution
a) The half-life is the average time it takes for half the remaining radioactive atoms in a sample to decay.
b) Working: 480 → 240 after 10 min, 240 → 120 after next 10 min, etc. Activity halves every 10 minutes, so the half-life = 10 min.
c) As radioactive atoms decay, there are fewer left that can decay. Since decay is random, but the number available falls, the measured rate (activity) falls, and this decrease follows an exponential pattern.