Question

A dye emits $75\%$ of the absorbed energy as fluorescence. The number of quanta absorbed and emitted out are in the ratio $2:3$. Find the wavelength of the emitted radiation if the absorbed radiation has a wavelength of $x\stackrel{o}{\text{A}}$.

• A. $x\stackrel{o}{\text{A}}$
• B. $0.5x\stackrel{o}{\text{A}}$
• C. $2x\stackrel{o}{\text{A}}$
• D. $4x\stackrel{o}{\text{A}}$

Answer 1

The correct option is C $2x\stackrel{o}{\text{A}}$

We know, E = $nhv$ = $\frac{nhc}{\lambda }$
where, n is the number of photons absorbed or emitted,
$\lambda$ is the wavelength.

Given: $E_{\text{emitted}}=\frac{75}{100}\times E_{\text{absorbed}}$

or, $n_1\times \frac{hc}{{\lambda }_1}=\frac{3}{4}\times n_2\times \frac{hc}{{\lambda }_2}$
where, $n_1$ and $n_2$ are the number of photons emitted and absorbed respectively.

And $n_1:n_2$ = $3:2$

$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{4}{3}\times \frac{n_1}{n_2}=\frac{4}{3}\times \frac{3}{2}$

$\Rightarrow \frac{{\lambda }_1}{x\stackrel{o}{\text{A}}}=\frac{2}{1}$

$\Rightarrow {\lambda }_1=2x\stackrel{o}{\text{A}}$