Question

A dye emits $50\%$ of the absorbed energy as fluorescence. If the number of quanta absorbed and the emitted out are in ratio $1:4$. Find the wavelength of 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. $4x\stackrel{o}{\text{A}}$
• D. $8x\stackrel{o}{\text{A}}$

Answer 1

The correct option is D $8x\stackrel{o}{\text{A}}$

We know, E = $nhv$ = $\frac{nhc}{\lambda }$ where n is the number of photon absorbed or emitted
$\lambda$ is the wavelength.
Given: $E_{\text{emitted}}=\frac{50}{100}\times E_{\text{absorbed}}$

or, $n_1\times \frac{hc}{{\lambda }_1}=\frac{1}{2}\times n_2\times \frac{hc}{{\lambda }_2}$
where $n_1$ and $n_2$ is the number of photons emitted and absorbed. And $n_1:n_2$ = $4:1$
$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{2}{1}\times \frac{n_1}{n_2}=\frac{2}{1}\times \frac{4}{1}$

$\Rightarrow \frac{{\lambda }_1}{x\stackrel{o}{\text{A}}}=\frac{8}{1}$

$\Rightarrow {\lambda }_1=8x\stackrel{o}{\text{A}}$