Question

Iodine-131 has a half life of 8.040 days how long will it take for a 40.0 grams sample of iodine 131 to decay to 0.75g

Answer 1

Answer:

$t=46.13days$

Explanation:

Hello there!

In this case, since the radioactive decay is considered as first-order kinetic model, whereby the remaining mass of the radioactive material involves the initial one, the rate constant and elapsed time:

$A=Ao*exp(-kt)$

As we were not initially given the rate constant, we can use the half-life to calculate it as follows:

$k=\frac{ln(2)}{8.040days}=0.08621days^{-1}$

Thus, we can calculated the elapsed time for the given conditions to obtain:

$t=\frac{ln(0.75g/40.0g)}{-0.08621days^{-1} }\\\\t=46.13days$

Regards!