Question

The bones of a saber-toothed tiger are found to have an activity per gram of carbon that is 12.9 % of what would be found in a similar live animal. How old are these bones?

Answer 1

Answer:

The bones are 16925 years old

Explanation:

We have to use the radioactive decay law and know that the half life of carbon-14 is $t_{\frac{1}{2}}=5730 \, years$. From this information we can know the decay rate of the carbon 14,

$\lambda=\frac{ln(2)}{t_{\frac{1}{2}}}=1.21\times 10^{-4} s^{-1}$

Now to know the age of the bones we must directly use the radioactive decay law:

$N(t)=N_0e^{-\lambda t}=0.129N_0$

Where the rightmost part of the equation comes from the statement that the activity found is just 12.9% of the activity that would be found in a similar live animal. This means that the number of carbon-14 atoms is just 12.9% of what it was at the moment the saber-toothed tiger died.

Solving for t we have:

$t=-\frac{ln(0.129)}{\lambda}=16925 \, years$