Question

An anthropologist finds bone that her instruments measure it as 0.061% 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

Let us assume that the rate of decay follows a 1st order reaction. Therefore the formula for rate of decay is:

A = Ao e^-kt                  ---> 1

Where,

A = final value after time t

Ao = initial value at t zero

k = rate constant

t = time elapsed

 

First let use find for the value of constant k. We know that the formula for half-life is:

t-half life = ln 2 / k

Finding for k:

5730 = ln 2 / k

k = 1.21 * 10^-4 yr^-1

 

Since it is stated that A = 0.00061 Ao, therefore substituting all the values into equation 1:

0.00061 Ao / Ao = e^(-1.21 * 10^-4 yr^-1 * t)

Finding for t:

t = 61,173.98 years

 

The person died about 61,174 years ago.