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. If the detection efficiency is 25%, how many radioactive nuclei are there at time t = 0?

Question

Quizplus · Accepted Answer

The observed counting rate is 3000 counts/s, which is 25% of the actual decay rate. Therefore, the actual decay rate is 3000 / 0.25 = 12000 decays/s. Using the decay constant λ = ln(2) / half-life, we find the number of nuclei N = decay rate / λ = 12000 / (ln(2) / 120) = 2.08 × 10^6.

A Radioactive Source Has a Half-Life of 2 Min