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# The threshold wavelength of a metal is $5800{\mathrm{A}}^{\mathrm{o}}$. The metal surface is illuminated with a light of wavelengthof $2800{\mathrm{A}}^{\mathrm{o}}$ and the electron is emitted with a certain energy. Calculate the potential required to bring the electron to rest.

Moderate
Solution

## Energy associated with a light of wavelength or $E=\frac{\left(6.626×{10}^{-34}\mathrm{Js}\right)\left(3×{10}^{8}{\mathrm{ms}}^{-1}\right)}{2800×{10}^{-10}\mathrm{m}}$$=7.099×{10}^{-19}\mathrm{J}$Threshold Energy,$\begin{array}{l}{E}_{0}=\frac{hc}{{\lambda }_{0}}\\ =\frac{\left(6.626×{10}^{-34}\mathrm{Js}\right)\left(3×{10}^{8}{\mathrm{ms}}^{-1}\right)}{5800×{10}^{-10}\mathrm{m}}\\ =3.427×{10}^{-19}\mathrm{J}\end{array}$Energy required to stop the electron = 2.292 eV$\therefore$ Potential required to bring the electron to rest = 2.292 eV.

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