# Curium-243 has a half-life of 285 days. In a sample of 5.6 grams of curium-243. how many grams will remain after 12 days?

May 30, 2017

approximately 5.4g

#### Explanation:

You can use the formula:

$N \left(t\right) = {N}_{\text{0"*(1/2)^(t/T_"1/2}}$

Where N is the amount of radioactive isotopes left to the time "t" (in this case t is measured in days). In this case measured in grams. ${T}_{\text{1/2}}$ is the half-life period. In this case 285 days.
${N}_{\text{0}}$ is the starting amout of radioactive isotopes, in this case 5.6 grams
Insert the numbers to get:

$N \left(12\right) = 5.6$g$\cdot {\left(\frac{1}{2}\right)}^{\frac{12}{285}} \approx 5.4$g

As a side note, I'm pretty sure Cm-243 has a lot longer half-life than that :P