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A near UV photon of $300 \mathrm{~nm}$ is absorbed by a gas and then re-emitted as two photons. One photon is red with wavelength of the second photon is
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The correct answer is:
$496 \mathrm{~nm}$
Energy values are additives.
$\begin{array}{l}
\mathrm{E}=\mathrm{E}_{1}+\mathrm{E}_{2} \\
\frac{\mathrm{hc}}{\lambda}=\frac{\mathrm{hc}}{\lambda_{1}}+\frac{\mathrm{hc}}{\lambda_{2}} \\
\frac{1}{300}=\frac{1}{760}+\frac{1}{\lambda_{2}} \\
\frac{1}{\lambda_{2}}=\frac{1}{300}-\frac{1}{760} \\
\lambda=495.6 \mathrm{~nm}=496 \mathrm{~nm}
\end{array}$
$\begin{array}{l}
\mathrm{E}=\mathrm{E}_{1}+\mathrm{E}_{2} \\
\frac{\mathrm{hc}}{\lambda}=\frac{\mathrm{hc}}{\lambda_{1}}+\frac{\mathrm{hc}}{\lambda_{2}} \\
\frac{1}{300}=\frac{1}{760}+\frac{1}{\lambda_{2}} \\
\frac{1}{\lambda_{2}}=\frac{1}{300}-\frac{1}{760} \\
\lambda=495.6 \mathrm{~nm}=496 \mathrm{~nm}
\end{array}$
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