A radioactive nuclei with decay constant \(0.5/\mathrm{s}\) is being produced at a constant rate of 100 nuclei/s. If at \(t=0\) there were no nuclei, the time when there are 50 nuclei is:
Show Hint
- \(1\ \mathrm{s}\)
- \(2\ln\left(\frac{4}{3}\right)\mathrm{s}\)
- \(\ln 2\ \mathrm{s}\)
- \(\ln\left(\frac{4}{3}\right)\mathrm{s}\)
The Correct Option is B
Solution and Explanation
\(\frac{R}{\lambda}=\frac{100}{0.5}=200\).
\(50=200\left(1-e^{-0.5t}\right)\Rightarrow e^{-0.5t}=\frac{3}{4}\).
\(0.5t=\ln\frac43\Rightarrow t=2\ln\frac43\ \mathrm{s}\).
Answer: (2) \(2\ln\left(\frac{4}{3}\right)\mathrm{s}\)
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