Question

If you have 100. mg of a radioactive isotope with a half-life of 10. years, how much of theisotope will you have left after 30. years?

Answer 1

In order to calculate the amount of the isotope that will be left after 30 years, we can use the formula:

$P=P_0\cdot(1+i)^t$

Where P is the final amount after t periods of time, P0 is the initial amount and i is the rate.

Since the half-life period of the isotope is 10 years, we can use i = -0.5 (that is, it will lose half its mass), t = 3 (since in 30 years we have 3 periods of 10 years) and P0 = 100.

So we have:

$\begin{gathered} P=100\cdot(1-0.5)^3 \\ P=100\cdot0.5^3 \\ P=100\cdot0.125 \\ P=12.5 \end{gathered}$

So the amount after 30 years is 12.5 mg.