A dye emits 50% of the absorbed energy as fluorescence. If the number of quanta absorbed and emitted — Atomic Structure Chemistry Question

💡 Solution & Explanation

Total emitted energy $E_{em} = 0.5 E_{abs}$. Thus, $n_{em} \frac{hc}{\lambda_{em}} = 0.5 n_{abs} \frac{hc}{\lambda_{abs}}$. Given $n_{abs}/n_{em} = 1/2$, so $n_{em} = 2 n_{abs}$. Substitute: $2 n_{abs} \frac{hc}{\lambda_{em}} = 0.5 n_{abs} \frac{hc}{x} \implies \frac{2}{\lambda_{em}} = \frac{0.5}{x} \implies \lambda_{em} = \frac{2x}{0.5} = 4x$ Å. Therefore, correct answer is C.