A sample of a radioactive isotope is found to have lost 19.8% of its original activity after 8.59 days.What is the decay constant of this isotope?

Question

Quizplus · Accepted Answer

The decay constant ($\lambda$) can be found using the formula for radioactive decay, which is $N = N_0 e^{-\lambda t}$, where $N$ is the remaining quantity of the substance, $N_0$ is the initial quantity, $t$ is the time, and $e$ is the base of the natural logarithm. Given that 19.8% of the isotope has decayed, 80.2% remains. Setting $N/N_0 = 0.802$ and $t = 8.59$ days, we can solve for $\lambda$. Rearranging the formula gives $\lambda = -\ln(N/N_0) / t$. Substituting the given values yields $\lambda \approx 0.026 d^{-1}$.

A Sample of a Radioactive Isotope Is Found to Have