Concept explainers
Interpretation: The age of artifact is to be determined.
Concept Introduction:
The rate constant (k) of the reaction is determined by:
t1/2 = 0.693k
The integrated rate law is as follows:
lnNtN0 = −ktNtN0 = N0e−kt
Here, N is the amount of sample left after time T and N0 is the initial amount of the sample.
As radioactivity is a first-order process, the rate of decay is directly proportional to the number of nuclei in the sample. Thus, the initial rate of decay (rate0) and the rate of decay at time t (ratet) can also be used in the integrated rate law:
Ratet =kNt ; Rate0 =kN0NtN0=Ratet/k Rate0/k =RatetRate0
Substitute the value of NtN0=RatetRate0 in the above integrated rate law equation to get,
lnRatetRate0=−kt
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