A certain radioactive isotope has a half-life of approximately 1500 years. How many years to the nearest year would be required for a given amount of this isotope to decay to 70% of that amount?
A) 2605 yr
B) 772 yr
C) 702 yr
D) 450 yr

Question

Quizplus · Accepted Answer

The amount of radioactive isotope remaining after t years is given by the formula A = A0 * (1/2)^(t/h), where A0 is the initial amount, h is the half-life, and t is the time elapsed. We want to find t such that A = 0.7A0. Substituting these values into the formula, we get 0.7A0 = A0 * (1/2)^(t/h). Dividing both sides by A0, we get 0.7 = (1/2)^(t/h). Taking the logarithm of both sides, we get log(0.7) = (t/h) * log(1/2). Solving for t, we get t = h * log(0.7) / log(1/2) = 1500 * log(0.7) / log(1/2) = 772 years.

A Certain Radioactive Isotope Has a Half-Life of Approximately 1500