A certain radioactive isotope has a half-life of approximately 950 years. How many years to the nearest year would be required for a given amount of this isotope to decay to 75% of that amount?
A) 394 years
B) 1900 years
C) 238 years
D) 319 years

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 = 0.75 * A0. Substituting these values into the formula, we get 0.75 * A0 = A0 * (1/2)^(t/h). Dividing both sides by A0, we get 0.75 = (1/2)^(t/h). Taking the logarithm of both sides, we get log(0.75) = (t/h) * log(1/2). Solving for t, we get t = h * log(0.75) / log(1/2) = 950 * log(0.75) / log(1/2) = 394 years.

A Certain Radioactive Isotope Has a Half-Life of Approximately 950