When a beam of photons of a particular energy was incident on a surface of a particular pure metal having work function ion = 40eV some emitted photo electrons had stopping potential equal to 22v and some had 12v and the rest had lower values calculate the wavelength of incident photons assuming that atleast one photoelectron is ejected with maximum possible kinetic energy

Dear Student,

Please find below the solution to the asked query:

Equation of the Einstein's Photoelectric Theory is,

$$\begin{gathered} K_{max}=h\nu -\varphi \Rightarrow e{V}_{max}=\frac{hC}{\lambda }-\varphi \\ \Rightarrow \frac{hC}{\lambda }=e{V}_{max}+\varphi \Rightarrow \frac{hC}{\lambda }=22+40 \left(in eV\right) \\ \Rightarrow \frac{12400}{\lambda \left(in {\displaystyle \stackrel{0}{A}}\right)}=62\Rightarrow \lambda =\frac{12400}{62}\Rightarrow \lambda =200 \stackrel{0}{A} \end{gathered}$$

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