Table 1 shows a quality-control record for a technetium tracer sample prepared in a hospital. Counts were measured for 60 s using the same detector geometry...
Question 1 Report
Table 1 shows a quality-control record for a technetium tracer sample prepared in a hospital. Counts were measured for 60 s using the same detector geometry. The background count is 12 counts per minute. A student must plot the corrected count against time on the grid provided, then use the graph to assess whether the sample has the expected half-life.
| Time after preparation / h | Count in 60 s |
|---|---|
| 0 | 972 |
| 6 | 492 |
| 12 | 252 |
| 18 | 132 |
| 24 | 72 |
(a) Plot the corrected count against time on the grid provided and draw a smooth curve of best fit. [3]
(b) State the half-life shown by the results. [1]
(c) Calculate the activity at time 12 h in Bq. [2]
(d) Explain why background radiation is subtracted from every count. [2]
(e) Calculate when the corrected count will first be below 30 counts per minute. [2]
(f) Describe why repeated count measurements at one time may not be identical. [2]
Answer Details
(a) Subtract the 12 counts per minute background before plotting. The corrected points are \((0,960)\), \((6,480)\), \((12,240)\), \((18,120)\), and \((24,60)\). A smooth decreasing curve through these points is required. [3]
(b) The corrected count halves every 6 h, so the half-life is 6 h. [1]
(c)\[252-12=240\text{ counts min}^{-1}\]
\[240/60=4\text{ Bq}\]
The activity at 12 h is 4 Bq. [2]
(d) The detector records radiation from the surroundings as well as from the tracer. Background subtraction gives the count and activity due only to the tracer. [2]
(e) At 24 h the corrected count is 60 counts per minute. One more half-life gives 30 counts per minute:
\[24+6=30\text{ h}\]
It first falls below 30 counts per minute after 30 h. [2]
(f) Radioactive decay is random, so the number of particles detected in equal time intervals fluctuates. [2]
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