Question

An anthropologist finds bone that her instruments measure it as 0.601% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die? The half life of carbon 14 is 5,730 years. Round your answer to the nearest thousand.

Answer 1

To solve this problem, let us first calculate the rate constant, k .Assuming the decay of C-14 is of 1st order reaction, the formula for half-life is given as:

t-half life = ln 2 / k

where k = rate constant of decay

5730 = ln 2 / k

k = 1.21 * 10^-4

The rate equation for a 1st order reaction is given as:

ln (A / Ao) = - k t

Where A = final amount of C-14, and Ao = initial amount of C-14

Since A = 0.00601 Ao therefore,

ln (0.00601) = - 1.21 * 10^-4 * t

t = 42,278.34 years

Answer: The person died around 42,278 years ago.