The wavelength of a photon is 1.4 Å. It collides with an electron. The energy of the scattered electron is 4.26 x 10^-16  J. Find the wavelength of photon after collision. $\left(\mathrm{Take}, \mathrm{h}=6.63\times {10}^{-34}\mathrm{J}-\mathrm{s}\right)$

Sol. Initial wavelength of photon is lland final wavelength of photon is ${\mathrm{\lambda }}_2.$

$$\begin{gathered} \therefore 4.26\times {10}^{-16}=\frac{\mathrm{hc}}{{\mathrm{\lambda }}_1}-\frac{\mathrm{hc}}{{\mathrm{\lambda }}_2} \\ \frac{\mathrm{hc}}{{\mathrm{\lambda }}_2}=\frac{\mathrm{hc}}{{\mathrm{\lambda }}_1}-4.26\times {10}^{-16} \\ \frac{6.63\times {10}^{-34}\times 3\times {10}^8}{{\mathrm{\lambda }}_2}=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{1.4\times {10}^{-9}}-4.26\times {10}^{-16} \\ \frac{6.63\times {10}^{-34}\times 3\times {10}^8}{{\mathrm{\lambda }}_2}=14.21\times {10}^{-16}-4.26\times {10}^{-16} \\ {\mathrm{\lambda }}_2=2\times {10}^{-10}\mathrm{m} \\ =2.0 \stackrel{\mathrm{o}}{\mathrm{A}} \end{gathered}$$