A certain radioactive isotope decays at a rate of 0.175% annually. Determine the half-life of this isotope, to the nearest year.
A) 396 yr
B) 172 yr
C) 4 yr
D) 286 yr

Question

Quizplus · Accepted Answer

The half-life of a radioactive isotope can be calculated using the formula $T_{1/2} = \frac{\ln(2)}{r}$, where $r$ is the decay rate per period. Given a decay rate of 0.175% annually, $r = 0.00175$ per year. Thus, $T_{1/2} = \frac{\ln(2)}{0.00175} \approx 396$ years.

A Certain Radioactive Isotope Decays at a Rate of 0