• # question_answer The maximum wavelength of a beam of light that can be used to produce photoelectric effect on a metal is 250 nm. The energy of the electrons in joule emitted from the surface of the metal when a beam of light of wavelength 200 nm is used, is A) $89.61\times {{10}^{-22}}$                      B) $69.81\times {{10}^{-22}}$C) $18.96\times {{10}^{-20}}$                      D) $19.86\times {{10}^{-20}}$

${{\lambda }_{0}}=250\times {{10}^{-9}}m$and$\lambda =200\times {{10}^{-9}}m$ $E=\frac{1}{2}m{{v}^{2}}=hv-h{{v}_{0}}=\frac{hc}{\lambda }-\frac{hc}{{{\lambda }_{0}}}$ $=hc\left[ \frac{1}{\lambda }-\frac{1}{{{\lambda }_{0}}} \right]$ $=6.62\times {{10}^{-34}}\times 3\times {{10}^{8}}\left[ \frac{1}{200}-\frac{1}{250} \right]\times \frac{1}{{{10}^{-9}}}$ $\therefore$$E=19.86\times {{10}^{-20}}J$ Hence, the correction option is [d].