Radioactivity involving background radiation - What is the reading on the detector after 68 hrs?

Answer: Option D

Note that the reading shown on the detector (536 counts per second) includes the sum of count rate from the radioactivity material and also the background radiation of 44 counts per second.

So to find the count rate purely from the radioactive material, you need to first minus 44 from the 536 = 492 counts per second.

Given that the half-life is 34 hrs, so in the duration of 68 hrs, there are 68/34 = 2 half-lives.

So 492 c/s after 1 half-life will becomes 492/2 =246 c/s

Another half-life later, it will becomes 246/2 =123 c/s

Note that 123 c/s is purely from the radioactive material, not the reading on the detector. Hence to find the reading on the detector, you need to add back the background count of 44 c/s = 123 + 44 = 167 c/s