The graph shows the variation of the activity \(A\) of a radioactive sample with time \(t\).
(a) Determine the half-life of the radioactive sample from the graph. [2]
(b) Calculate the decay constant \(\lambda\) for this sample. [2]
(c) Determine the activity of the sample at \(t = 5.0\) hours. [1]
(d) Another sample of the same isotope has an initial activity of 1600 Bq. Based on the provided diagram, explain how its activity will vary with time relative to the original sample. [1]
Part a
2 minutes
2 marks
Question
Determine the half-life of the radioactive sample from the graph. [2]
Hint Hint
Hint
Identify the time taken for the activity to drop from 800 Bq to 400 Bq.
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2.0 hours
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Part b
2 minutes
2 marks
Question
Calculate the decay constant \(\lambda\) for this sample. [2]
Hint Hint
Hint
Use the formula \(\lambda = \frac{\ln(2)}{T_{1/2}}\).
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\(\lambda \approx 0.347\ text{hour}^{-1}\)
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Part c
1 minutes
1 marks
Question
Determine the activity of the sample at \(t = 5.0\) hours. [1]
Hint Hint
Hint
Apply the decay formula \(A = A_0e^{-\lambda t}\) with \(A_0 = 800\) Bq and \(\lambda \approx 0.347\ text{hour}^{-1}\).
Answer Answer
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Approximately 141 Bq
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Part d
1 minutes
1 marks
Question
Another sample of the same isotope has an initial activity of 1600 Bq. Based on the provided diagram, explain how its activity will vary with time relative to the original sample. [1]
Hint Hint
Hint
Recognize that the second sample decays with the same rate; its activity values will be proportionally higher than those of the original sample.
Answer Answer
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The interpretation indicates that while the second sample begins at 1600 Bq, it decays exponentially at the same rate, meaning at any given time its activity is double that of the original sample.
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