Physics - Modern Physics Question with Solution | TestHub

Given: work function $\varphi$ of metal $=2.28\mathrm{eV}$ Wavelength of light $\lambda =500\mathrm{nm}=500\times 10^{-}$ $9\mathrm{m}$ $$\begin{array}{l}{\mathrm{KE}}_{\max }=\frac{\mathrm{hc}}{\lambda }-\varphi \\ {\mathrm{KE}}_{\max }=\frac{6.6\times 10^{-34}\times 3\times 10^8}{5\times 10^{-7}}-2.82\\ {\mathrm{KE}}_{\max }=2.48-2.28=0.2\mathrm{eV}\\ {\lambda }_{\min }=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\sqrt{2\mathrm{m}(\mathrm{KE}{)}_{\max }}}\end{array}$$ $$\begin{array}{l}=\frac{\frac{20}{3}\times 10^{-34}}{\sqrt{2\times 9\times 10^{-31}\times 0.2\times 1.6\times 10^{-19}}}\\ {\lambda }_{\min }=\frac{25}{9}\times 10^{-9}\\ =2.80\times 10^{-9}\mathrm{nm}\therefore \lambda \ge 2.8\times 10^{-9}\mathrm{m}\end{array}$$