# Given the following chart, what will the rock contain after 40.000 years or 2 half-lives?

Mar 5, 2017

There is $5 m g$ unstable isotope and $15 m g$ stable isotope.

#### Explanation:

After one half-life, the amount of unstable isotope halves. After another half-life, that amount halves again, so

${t}_{\frac{1}{2}} \to \frac{20}{2} = 10 m g$

$2 {t}_{\frac{1}{2}} \to \frac{10}{2} = 5 m g$

The unstable product decays into the stable product and the total mass remains the same. Adding together the mass of unstable and stable isotopes, it is always $20 m g$, so

$20 - 5 = 15 m g$ of stable isotope after 40,000 years.