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A radioactive nuclei with decay constant 0.5/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 :

$(a)\;1\;s\qquad(b)\;2 ln(\large\frac{4}{3})\;s \qquad(c)\;\normalsize ln 2 \;s\qquad(d)\; ln(\large\frac{4}{3})\;s $

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