A certain radioactive isotope decays to one sixteenth of its original amount in 4.0 hours.What is its mean lifetime?

Question

Quizplus · Accepted Answer

The mean lifetime ($\tau$) of a radioactive isotope is related to its half-life ($t_{1/2}$) by the equation $\tau = \frac{t_{1/2}}{\ln(2)}$. Given that the isotope decays to one sixteenth (or $(1/2)^4$) of its original amount in 4 hours, it has a half-life of $4 hours / 4 = 1 hour$. Substituting into the equation gives $\tau = \frac{1}{\ln(2)} \approx 1.44$ hours, which rounds to 1.4 hours.

A Certain Radioactive Isotope Decays to One Sixteenth of Its