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JEE Main 2014 · 11 Apr · Shift 1, Physics question 27

A radioactive nuclei with decay constant 0.5/s is being produced at a constant rate of 100 nuclei/s. If at t=0t=0 there were no nuclei, the time when there are 50 nuclei is :

Choose one option
Answer and worked solution

Official answer: B

dNdt=100−0.5N\dfrac{dN}{dt}=100-0.5N with N(0)=0N(0)=0 gives N=200(1−e−0.5t)N=200\left(1-e^{-0.5t}\right).

N=50N=50 when e−0.5t=34e^{-0.5t}=\frac34, i.e. t=2ln⁡43t=2\ln\frac43 s.

Topics:Radioactive decay
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