`._(84)Po^(218) (t_(1//2) = 3.05 min)` decays to `._(82)Pb^(214) (t_(1//2) = 2.68 min)` by `alpha` emisison while `Pb^(214)` is `beta`-emitter. In an experiment starting with `1 g` atom of pure `Po^(218)`, how much time would be required for the concentration of `Pb^(214)` to reach maximum?

Explanation

To solve the problem of how much time is required for the concentration of lead-214 (Pb-214) to reach its maximum after the decay of polonium-218 (Po-218), we will follow these steps:

### Step 1: Write the Decay Reactions
Polonium-218 decays to lead-214 through alpha emission:
\[ _{84}^{218}\text{Po} \rightarrow _{82}^{214}\text{Pb} + _{2}^{4}\text{He} \]

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