Question

A seashell has only 3.1% of its c-14 left. The half life of c-14 is 5740 years. How old is the seashell

Answer 1

The seashell is 28747.96 years old.

Why?

If we need to calculate how old is something, we can use the equation for radioactive decay rate. It's possible using the C-14 half-life (5740 years) as reference. Remember, C-14 is used because all the living things take up the element from the atmosphere, when an organism dies, the amount of carbon starts to decay (very slowly).

Decay rate half life:

$N_{t}=N_{o}*e^{-l*t}$

Where,

$N_o}$ is the initial number of atoms (undecayed)

$N_{t}$ is the the number of atoms at time (undecayed)

$l$ is the decay rate

Now, isolating the decay rate of the formula, we have:

{$N_{t}=N_{o}*e^{-l*t}\\\\ln(\frac{N_{t}}{N_{o}})=-l*t$

Also, we can get the value of the decay rate (half life), using the following formula:

$l=\frac{0.693}{5740}=1.207x10^{-4}$

Then, using the given information, we have:

$ln(\frac{3.1}{100})=-1.207x10^{-4}*t$

$-3.47=-1.207x10^{-4}*t$

$-3.47=-1.207x10^{-4}*t\\\\t=\frac{-3.47}{1.207x10^{-4}}=28748.96years$

Hence, the seashell is 28748.96 years old.

Have a nice day!