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# grams

Final mass #M_f = 23.25# grams.

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

#M_f = M_0timese^(-ktimest)#

#ln(M_f/M_0) = -ktimest#

#ln(23.25/372) = -ktimes135#

#-2.7726 = -ktimes135#

#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.