A certain radioactive isotope decays from 70 grams to 45 grams in 27 years. What is the half-life of the isotope?
A) 40.16 years
B) 42.36 years
C) 48.31 years
D) 50.02 years
E) 36.25 years

Question

Quizplus · Accepted Answer

The half-life of a radioactive isotope can be calculated using the formula $N = N_0 \times (1/2)^{\frac{t}{T}}$, where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life. Rearranging the formula to solve for $T$, we get $T = \frac{t}{\log_2(\frac{N_0}{N})}$. Substituting $N_0 = 70$ grams, $N = 45$ grams, and $t = 27$ years, we can solve for $T$. The calculation yields a half-life close to 42.36 years.

A Certain Radioactive Isotope Decays from 70 Grams to 45