When any radioactive dating method is used, experimental error in the measuremen

Question

When any radioactive dating method is used, experimental error in the measurement of the sample's activity leads to error in the estimated age. In an application of the radiocarbon dating technique to certain fossils, an activity of 0.110 Bq per gram of carbon is measured to within an accuracy of 15.0 percent. Find (a) the age of the fossils and (b) the maximum error (both in years) in the value obtained. Assume that there is no error in the 5730-year half-life of 6C14 nor in the value of 0.23 Bq per gram of carbon in a living organism.

Explanation / Answer

Given data

activity of carbon in certain fossils A = 0.10 Bq per gram

accuracy = 15.0 percent = 0.15

halflife time T = 5730-year

activity of carbon in a living organism A0 = 0.23 Bq per gram

Solution :-

a) A = A0*e(-*t).

where
is the decay constant
= ln2/T,

where T is half-life

A/A0 = e(- ln2*t/T).
ln(A/A0)= - ln2*t/T
ln(0.11 / 0.23) = -ln2*t / 5730.

ln(0.4782) = -ln2*t/5730.
-0.7376 = -ln2*t/5730.
t = -0.7376*5730 / -ln2

= 6097.46 years

b) 15% 6097.46 = 914.62 years
So Error is 6097.46 ± 914.62 years

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