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Relative Velocity

A certain dye...

Question

A certain dye absorbs lights of $λ = 400 n m$ and then fluorescence light of wavelength $500 n m$ . Assuming that under the given condition, $40 %$ of the absorbed energy is re-emitted as fluorescence, the ratio of quanta absorbed to the number of quanta emitted out is ______.

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Solution

By given conditions:

$n_{1} \times \frac{h c}{400} \times 0.4 = n_{2} \times \frac{h c}{500}$

$\frac{n_{1}}{n_{2}} = \frac{400}{0.4 \times 500}$

$\frac{n_{1}}{n_{2}} = 2$

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