Solve the problem.
-A certain radioactive isotope has a half-life of approximately 1250 years. How many years to the nearest year would be required for a given amount of this isotope to decay to 20% of that amount?
A) 402 years
B) 1000 years
C) 2902 years
D) 2882 years

Question

Quizplus · Accepted Answer

To find the time required for a radioactive isotope to decay to a certain percentage, we use the formula: $ t = \frac{\ln(\text{final amount/original amount})}{\ln(0.5)} \times \text{half-life} $. Here, the final amount is 20% of the original, so $ t = \frac{\ln(0.2)}{\ln(0.5)} \times 1250 \approx 2902 $ years.

Solve the Problem. -A Certain Radioactive Isotope Has a Half-Life of Approximately 1250