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Carbon-14 is a radioactive isotope that occurs naturally - Edexcel - GCSE Physics - Question 4 - 2013 - Paper 1
Question 4
Carbon-14 is a radioactive isotope that occurs naturally. Scientists use carbon-14 to help find the age of old pieces of wood. This technique is called carbon datin... show full transcript
Worked Solution & Example Answer:Carbon-14 is a radioactive isotope that occurs naturally - Edexcel - GCSE Physics - Question 4 - 2013 - Paper 1
Step 1
Step 2
Sketch a graph to show how the activity of a radioactive isotope changes with time.
Answer
The graph should depict a decreasing exponential curve that starts from point P, reflecting the decay of the radioactive isotope over time. The y-axis represents activity, and the x-axis represents time, with the curve approaching zero but never quite reaching it.
Step 3
Calculate the activity of the carbon-14 in the comb when it was new.
Answer
To calculate the initial activity of carbon-14 when the comb was new, we can use the decay formula:
A = A_0 e^{- rac{ au}{T_{1/2}}}
Where:
- = final activity (0.55 Bq)
- = initial activity
- = age of sample (11,400 years)
- = half-life (5,700 years)
Rearranging gives:
A_0 = A e^{ rac{ au}{T_{1/2}}}
Substituting the values:
A_0 = 0.55 e^{ rac{11400}{5700}} = 0.55 e^{2}
Calculating this gives us:
Step 4
Explain why this is necessary to improve the accuracy of the investigation.
Answer
Taking several readings of background radiation helps ensure that the measurements of the radioactive sample are accurate. Background radiation can vary due to environmental factors, and averaging multiple readings helps to minimize random fluctuations, making the results more reliable.
Step 5
Suggest a reason for this change.
Answer
The reason for measuring the mass of undecayed carbon-14 instead of its activity is that the activity can be very low and difficult to measure accurately against background radiation. Measuring the mass of undetected carbon-14 provides a more direct and reliable way of determining the age of an object.