A radioactive source has a half-life of 2 min.At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s.The counting rate at t = 10 min will be
A)1500 counts/s
B)750 counts/s
C)375 counts/s
D)188 counts/s
E)94 counts/s

Question

Quizplus · Accepted Answer

The half-life of the radioactive source is 2 minutes, meaning its activity (or counting rate) halves every 2 minutes. At t = 10 minutes, 5 half-lives have passed (10 minutes / 2 minutes per half-life = 5 half-lives). Therefore, the counting rate decreases by a factor of $2^5 = 32$. The initial counting rate is 3000 counts/s, so the counting rate at t = 10 minutes is $3000 / 32 = 93.75$ counts/s, which rounds to 94 counts/s, option E.

A Radioactive Source Has a Half-Life of 2 Min