Question

The ratio of carbon-14 to nitrogen-14 is an artifact is 1:3. Given that half-life of carbon-14 is 5730years, how old is the artifact?

Answer 1

Answer:

9155 years old

Explanation:

We use the following expression for the decay of a substance:

$N = N_0\,\,e^{-k*t}$

So we first estimate the value of k knowing that the half-life of the C14 is 5730 years:

$N = N_0\,\,e^{-k*t}\\N_0/2=N_0\,\,e^{-k*5730}\\1/2 = e^{-k*5730}\\ln(1/2)=-k*5730\\k= 0.00012$

so, now we can estimate the age of the artifact by solving for"t" in the equation:

$1/3=e^{-0.00012*t}\\ln(1/3)= -0.00012*t\\t=9155. 102$

which we can round to 9155 years old.