# Question #cf933

##### 2 Answers

The artifact would b 17 190 years old.

You calculate the number of half-lives and multiply by the length of one half-life.

The number of half-lives is

For each half-life, you divide the total amount of the isotope by 2, so

You can rearrange this to

If original amount was 100 %, and 12.5 % of the nuclide remains undecayed, we have

The artifact would be **17,190 years** old.

The half-life of a radioactive isotope expresses the time needed for a sample of that isotope to reach **half of its original mass**.

So, if you're dealing with a sample of carbon-14, you know that it's going to take **5,730 years** for that sample to reach half of the mass it started with.

Moreover, after another 5,730 years, the sample will once again reach half of the mass it started with. But this time, the mass it started with is **half** of the initial mass, so that means that you're going to be left with **one quarter** of the initial mass after **2** half-lives pass.

Notice that the problem doesn't provide an initial mass, which means that it's not important in the calculations. Think of it like this: *regardless* of how much carbon-14 you start with, you'll be left with

*50% of the initial mass*#-># after**1**half-life;*25% of the initial mass*#-># after**2**half-lives;*12.5% of the initial mass*#-># after**3**half-lives;*6.25% of the initial mass*#-># after**4**half-lives.

And so on.

In your case, you know that you're left with **12.5%** of the initial mass of carbon-14, which means that **3 half-lives** must have passed. This means that

have passed since the artifact was made.