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

`t=46.13days`

Step-by-step 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=(ln(2))/(8.040days)=0.08621days^(-1)`

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

`t=(ln(0.75g/40.0g))/(-0.08621days^(-1) )\\\\t=46.13days`

Regards!