Question

the maximum wavelength of a beam of light can be used to produce photo electric effect on a metal is 250nm. the energy of the electrons in joule emitted from the surface of the metal when a beam of light of wavelength 200nm is used is?

Answer 1

$$\begin{gathered} \mathrm{Energy}\mathrm{of}\mathrm{incident}\mathrm{light}: \\ \mathrm{E}=\frac{\mathrm{hc}}{\mathrm{\lambda }} \\ =\frac{\left(6.6\times {10}^{-34}\right)\left(3\times {10}^8\right)}{200\times {10}^{-9}} \\ =9.9\times {10}^{-19}\mathrm{J} \\ \mathrm{Work}\mathrm{function}: \\ \mathrm{W}=\frac{\mathrm{hc}}{{\mathrm{\lambda }}_{\mathrm{o}}} \\ =\frac{\left(6.6\times {10}^{-34}\right)\left(3\times {10}^8\right)}{250\times {10}^{-9}} \\ =7.92\times {10}^{-19}\mathrm{J} \\ \mathrm{Energy}\mathrm{of}\mathrm{the}\mathrm{emitted}\mathrm{electrons}: \\ \mathrm{KE}=\mathrm{E}-\mathrm{W} \\ =9.9\times {10}^{-19}\mathrm{J}-7.92\times {10}^{-19}\mathrm{J} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{98}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{19}}\mathbf{}\mathbf{J} \end{gathered}$$