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# $\mathrm{A}$ quanta of light having energy $\mathrm{E}$, has a wavelength equal to . Find the wavelength of photon that corresponds to energy .

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## Energy of first light,                  ${E}_{1}=\frac{hc}{{\lambda }_{1}}$                                   Energy of second light,                   ${E}_{2}\left(=5{E}_{1}\right)=\frac{hc}{{\lambda }_{2}}$                       Dividing equations ($\mathrm{A}$) and ($\mathrm{B}$), we get                     $\frac{{E}_{1}}{{E}_{2}}=\frac{hc}{{\lambda }_{1}}×\frac{{\lambda }_{2}}{hc}=\frac{{\lambda }_{2}}{{\lambda }_{1}};\frac{{E}_{1}}{5{E}_{1}}=\frac{{\lambda }_{2}}{750\mathrm{nm}}$Hence,                              ${\lambda }_{2}=\frac{750\mathrm{nm}}{5}=150\mathrm{nm}$.

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