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.
