# At the beginning of an experiment, a scientist has 372 grams of radioactive goo. After 135 minutes, her sample has decayed to 23.25 grams. What is the half-life of the goo in minutes?

Jul 31, 2018

Half life question

#### Explanation:

Initial mass ${M}_{0} = 372$ grams

Final mass ${M}_{f} = 23.25$ grams.

Exponential decay says (k is decay constant and t is time)

${M}_{f} = {M}_{0} \times {e}^{- k \times t}$

$\ln \left({M}_{f} / {M}_{0}\right) = - k \times t$

$\ln \left(\frac{23.25}{372}\right) = - k \times 135$

$- 2.7726 = - k \times 135$

$k = 0.0205$ ${\left(\min\right)}^{-} 1$

Now we can calculate half-time:

$\ln \left(\frac{50}{100}\right) = - k \times t$

$\frac{- 0.693}{- 0.0205} = 33.81$ minutes.

Half time of goo is 33.81 minutes.