A radioactive source is freshly prepared. It is found that it emits radiation of intensity which is 128 times the permissible safe level. The half life of this sample is 3 hours. Find the minimum time after which it would be possible to work safely with this radioactive source.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 21 h
The intensity of the radiation from a radioactive source falls like its activity: it halves in every half-life, so after n half-lives it is \( I = I_0\left(\frac{1}{2}\right)^{n} \). It is safe to work with the source when the intensity has fallen to the permissible level, that is to \( \frac{1}{128} \) of the initial value.
\( \displaystyle \left(\frac{1}{2}\right)^{n} = \frac{1}{128} = \left(\frac{1}{2}\right)^{7} \Rightarrow n = 7 \)
\( t = nT_{1/2} = 7\times3\,\mathrm{h} = 21\,\mathrm{h} \)