We’re being asked to determine the time it takes for the decay rate of Tl-201 to fall from 5.88×104 /s to 303/s.
Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:
[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:
We will do the following steps to solve the problem:
Step 1: Calculate the decay constant, k
Step 2: Calculate the time
A sample of Tl-201 has an initial decay rate of 5.88×104 /s .
How long will it take for the decay rate to fall to 303 /s ? (Tl-201 has a half-life of 3.042 days.)
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