A dye absorbs a photon of wavelength $\lambda$ and reemits the same energy into two photons of wavelength…

A dye absorbs a photon of wavelength $\lambda$ and reemits the same energy into two photons of wavelength $\lambda_{1}$ and $\lambda_{2}$ respectively. The wavelength $\lambda$ is related with $\lambda_{1}$ and $\lambda_{2}$ as:
  1. $\lambda=\frac{\lambda_{1}+\lambda_{2}}{\lambda_{1} \lambda_{2}}$
  2. $\lambda=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}}$
  3. $\lambda=\frac{\lambda_{1}^{2} \lambda_{2}^{2}}{\lambda_{1}+\lambda_{2}}$
  4. $\lambda=\frac{\lambda_{1} \lambda_{2}}{\left(\lambda_{1}+\lambda_{2}ight)^{2}}$

Solution

$\mathrm{E}=\mathrm{E}_{1}+\mathrm{E}_{2} ; \quad \frac{\mathrm{hc}}{\lambda}=\frac{\mathrm{hc}}{\lambda_{1}}+\frac{\mathrm{hc}}{\lambda_{2}}$
$\Rightarrow \frac{\mathrm{hc}}{\lambda}=\mathrm{hc}\left(\frac{\lambda_{2}+\lambda_{1}}{\lambda_{1} \lambda_{2}}ight) ; \quad \lambda=\frac{\lambda_{1} \lambda_{2}}{\lambda_{1}+\lambda_{2}}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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