A chunk of radioactive material decays from a mass of 450 grams to 165 grams in two weeks, (14 days). Find the half-life time and the amount of material left after 70 days.

Answer 1

We will use the radioactive decay equation, P(t) = P₀e^kt.

First we will find the rate. We are told that 450 gram disintegrates to 165 gram, so we have P(0) = 450 and P(14) = 165. However, P(14) can also be expressed as:

P(14) = 165 = 450e^k14

165/450 = e^k14

ln(165/450) = k14

1/14ln(165/450) = k

-0.07 = k

Now we need to find the half-life:

225 = 450e^k14

225/450 = e^-0.07t

ln(225/450) = -0.07t

 ln(225/450)/-0.07 = t

9.9 days = t

Now, we will find the amount after 70 days has passed using the following equation:

P(t) = 450 e^-0.07(70) = 450 e^-4.9 = 3.35 grams