Carbon dating is a technique for discovering the age of ancient once-living objects, such as bone, charcoal or a piece of wood, by measuring the amount of the radio-active isotope Carbon-14 ( $^{14}C$ ) that it contains.

Whilst plants and animals are alive their Carbon-14 remains constant, but when they die it decreases due to radioactive decay.

The amount, A, of Carbon-14 in an object t thousand years after it dies is given by the formula:

$A=15.3\times\(0.886)^t$

(The quantity A measures the rate of Carbon-14 atom disintegration and this is measured in “counts per minute per gram of carbon” cpm/g)

(a) Using a calculator, draw a table of values to show how the amount of Carbon-14 in an object varies with time. (Correct to 2 decimal places).

(b) Draw a graph of this data.

(c) Imagine that you have a fresh sample of tree wood. What is the rate of Carbon-14 atom disintegration?

(d) Imagine you have a sample of charcoal from Stonehenge and it is 4000 years old. What is the rate of Carbon-14 atom disintegration?

(e) Charcoal from the famous Lascaux caves in France gave a count of 2.34 cpm/g. Estimate the date of formation of the charcoal.

(f) Investigate "half-life" of a radioactive isotope.

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