Problem: An artifact showed a carbon­-14 decay rate of 13.8 disintegrations/min per gram of carbon. Carbon-­14 has a half­-life of 5715 years, and currently living organisms decay at the rate of 15.3 disintegrations/min per gram of carbon. What is the approximate age (yr) of the artifact?a. 658b. 581c. 423d. 851e. 42328

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We’re being asked to determine the approximate age (yr) of the artifact that showed a carbon­-14 decay rate of 13.8 disintegrations/min per gram of carbon. Carbon-­14 has a half­-life of 5715 years, and currently living organisms decay at the rate of 15.3 disintegrations/min per gram of carbon


Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:


ln [N]t=-kt+ln [N]0


where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration


Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half


The half-life of a first-order reaction is given by:


t12=ln 2k


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Problem Details

An artifact showed a carbon­-14 decay rate of 13.8 disintegrations/min per gram of carbon. Carbon-­14 has a half­-life of 5715 years, and currently living organisms decay at the rate of 15.3 disintegrations/min per gram of carbon. What is the approximate age (yr) of the artifact?

a. 658
b. 581
c. 423
d. 851
e. 42328

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