Physics - Modern Physics Question with Solution | TestHub

Given : work function$\varphi$of metal$=2.28 \mathrm{eV}$

Wavelength of light$\lambda =500 \mathrm{nm}=500\times {10}^{-9}\mathrm{ m}$

$K{E}_{max}=\frac{hc}{\lambda }-\varphi$

$K{E}_{max}=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{5\times {10}^{-7}\times 1.6\times {10}^{-19}}-2.82$

$K{E}_{max}=2.48-2.28=0.2\mathrm{ eV}$

${\lambda }_{min}=\frac{h}{p}=\frac{h}{\sqrt{2m{\left(KE\right)}_{max}}}$

$=\frac{\frac{20}{3}\times {10}^{-34}}{\sqrt{2\times 9\times {10}^{-31}\times 0.2\times 1.6\times {10}^{-19}}}$

${\lambda }_{min}=\frac{25}{9}\times {10}^{-9}$

$$\begin{gathered} =2.80\times {10}^{-9} \mathrm{nm} \\ \therefore \lambda \ge 2.8\times {10}^{-9}\mathrm{ m} \end{gathered}$$