Question

9. The half-life of radon-222 is 3.8 days. How much of a 100. g sample is left after 45 days?

Answer 1

In order to calculate the amount of radon-222 left after 45 days, we can use the formula:

$P=P_0\cdot0.5^{\frac{t}{n}}$

Where P is the final amount after t days, P0 is the initial amount, t is the number of days and n is the period of half-life.

So, using P0 = 100, t = 45 and n = 3.8, we have:

$\begin{gathered} P=100\cdot0.5^{\frac{45}{3.8}} \\ P=100\cdot0.5^{11.842} \\ P=0.0272 \end{gathered}$

So the amount left after 45 days is 0.0272 grams.