At a particular time, a radioactive source A has a strength of 1.60 *10¹¹ Bq and a half-life of 8.00 days, and a radioactive source B has a strength of 6.40 *10¹¹ Bq. The two sources have the same strength 30.0 days later. The half-life of source B is A) 35.7 days. B) 24.7 days. C) 17.2 days. D) 7.53 days. E) 5.22 days.

Question

Quizplus · Accepted Answer

The decay of radioactive sources follows the formula N(t) = N0 * (1/2)^(t/T), where N0 is the initial strength, t is time, and T is the half-life. For source A, after 30 days, its strength is 1.60 * 10^11 * (1/2)^(30/8). For source B, let T be the half-life, its strength after 30 days is 6.40 * 10^11 * (1/2)^(30/T). Setting these equal and solving for T gives approximately 17.2 days.

At a Particular Time, a Radioactive Source a Has a Strength