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 0.130 Bq per gram of carbon is measured to within an accuracy of 14.0 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

A=A?e(-?t).
? is the decay constant (not the wavelength!!!)
?=ln2/T, where T is half-life
A/A?= e(- ln2t/T).
ln(A/A?)= - ln2t/T
ln(0.13/0.23)=ln(0.565)
= - 0.571 = -ln2 t/5730.
t=0.5715730/ln2=4720.25 years

14/100 4720.25 =660.84 years
Ans. 4720.25660.84 years

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