Problem 3.215

Having been operated long enough, the ionizer producing \(n_{i}=3.5 \cdot 10^{9} \mathrm{~cm}^{-3} \cdot \mathrm{s}^{-1}\) of ion pairs per unit volume of air per unit time was switched off. Assuming that the only process tending to reduce the number of ions in air is their recombination with coefficient \(r=1.67 \cdot 10^{-6} \mathrm{~cm}^{3} / \mathrm{s}\), find how soon after the ionizer's switching off the ion concentration decreases \(\eta=2.0\) times.