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?

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Answer 1 · 2018-07-31T08:19:10

Half life question

Initial mass $M_{0} = 372$ $M_0 = 372$ grams

Final mass $M_{f} = 23.25$ $M_f = 23.25$ grams.

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

$M_{f} = M_{0} \times e^{- k \times t}$ $M_f = M_0timese^(-ktimest)$

$ln (\frac{M_{f}}{M_{0}}) = - k \times t$ $ln(M_f/M_0) = -ktimest$

$ln (\frac{23.25}{372}) = - k \times 135$ $ln(23.25/372) = -ktimes135$

$- 2.7726 = - k \times 135$ $-2.7726 = -ktimes135$

$k = 0.0205$ $k=0.0205$ $(min)^-1$

Now we can calculate half-time:

$ln(50/100) = -ktimest$

$(-0.693)/(-0.0205)= 33.81$ minutes.

Half time of goo is 33.81 minutes.