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A particular type of nucleus whose decay...

A particular type of nucleus whose decay constant is `lambda` is produced at a steady rate of `p` nuclei per second. Show that the number of nuclei `N` present `t` second after the production starts is `N=(P)/(lambda)[1-e^(~lambdat)]`.

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To solve the problem step by step, we need to derive the expression for the number of nuclei \( N \) present \( t \) seconds after production starts. ### Step 1: Understand the decay and production rates We know that: - The production rate of the nuclei is \( p \) nuclei per second. - The decay constant of the nuclei is \( \lambda \). The activity (rate of decay) of the nuclei is given by: ...
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