Choose the one alternative that best completes the statement or answers the question.
-A certain radioactive isotope decays at a rate of $0.2 \%$ annually. Determine the half-life of this isotope, to the nearest year.
A) $151 \mathrm { yr }$
B) $347 \mathrm { yr }$
C) $3 \mathrm { yr }$
D) $250 \mathrm { yr }$

Question

Quizplus · Accepted Answer

The half-life can be calculated using the formula $ t_{1/2} = \frac{\ln(2)}{r} $, where $ r $ is the decay rate. Here, $ r = 0.002 $ (0.2% as a decimal), so $ t_{1/2} \approx \frac{0.693}{0.002} \approx 346.5 $, which rounds to 347 years.

Choose the One Alternative That Best Completes the Statement or Answers