The graph in Fig. 1 shows measurements from a tracer used to find a small leak in a district-heating water pipe. A student measures the activity of a sample...
Question 1 Report
The graph in Fig. 1 shows measurements from a tracer used to find a small leak in a district-heating water pipe. A student measures the activity of a sample of the tracer at regular intervals. The measuring system records gamma radiation, which can pass through the pipe wall.
(a) State the activity of the sample at 12 h. [1]
(b) Calculate the half-life of this radioactive isotope. [2]
(c) Calculate the activity after 18 h as a fraction of its activity at 0 h. [2]
(d) Describe the change in the number of undecayed nuclei in the sample during the first 18 h. [2]
(e) Explain why the activity cannot be predicted exactly for one particular nucleus. [2]
Answer Details
(a) At 12 h, the graph gives an activity of 20 kBq. [1]
(b) The initial activity is 80 kBq. It falls to 40 kBq, half its initial value, at 6 h. Therefore the half-life is 6 h. [2]
(c) At 18 h the activity is 10 kBq:
\[\frac{10}{80}=\frac18\]
The activity is one eighth of its activity at 0 h. [2]
(d) The number of undecayed nuclei decreases. It halves every 6 h, so after 18 h, which is three half-lives, one eighth remains. [2]
(e) Decay of an individual nucleus is random. It is only possible to state the probability that it will decay during a particular time interval, not exactly when it will decay. [2]
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