A radioactive nucleus with decay constant λ decays to a stable daughter nucleus. (a) Show that t

(a) The rate of decay of the parent nuclei is proportional to the number of parent nuclei presen

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A radioactive nucleus with decay constant $\lambda$ decays to a stable daughter nucleus. (a) Show that the number of daughter nuclei, $N_{2},$ increases with time according to the expression $$N_{2}=N_{01}\left(1-e^{-\lambda t}\right)$$ where $N_{01}$ is the initial number of parent nuclei. (b) Starting with $10^{6}$ parent nuclei at $t=0,$ with a halflife of $10 \mathrm{h},$ plot the number of parent nuclei and the number of daughter nuclei as functions of time over the interval 0 to $30 \mathrm{h}$.

          A radioactive nucleus with decay constant $\lambda$ decays to a stable daughter nucleus. (a) Show that the number of daughter nuclei, $N_{2},$ increases with time according to the expression $$N_{2}=N_{01}\left(1-e^{-\lambda t}\right)$$ where $N_{01}$ is the initial number of parent nuclei.
(b) Starting with $10^{6}$ parent nuclei at $t=0,$ with a halflife of $10 \mathrm{h},$ plot the number of parent nuclei and the number of daughter nuclei as functions of time over the interval 0 to $30 \mathrm{h}$.

Added by Alvaro C.

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