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  • The maximum kinetic energy of the photoelectrons emitted is doubled when the wavelength of light incident on the photosensitive surface changes from &nb

The maximum kinetic energy of the photoelectrons emitted is doubled when the wavelength of light incident on the photosensitive surface changes from \lambda _{1} to \lambda _{2}.  Deduce expressions for the threshold wavelength and work function for the metal surface in terms of \lambda _{1} and \lambda _{2}

 

 

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\\K_{max}=\frac{hc}{\lambda_1}-\phi_0=hc(\frac{1}{\lambda_1}-\frac{1}{\lambda_0})\\\lambda=\lambda_2\\2K_{max}=hc(\frac{1}{\lambda_2}-\frac{1}{\lambda_0})\\\frac{K_{max}}{2K_max}=\frac{(\frac{1}{\lambda_1}-\frac{1}{\lambda_0})}{(\frac{1}{\lambda_2}-\frac{1}{\lambda_0})}\\\\\lambda_0=\frac{\lambda_1\lambda_2}{2\lambda_2-\lambda_1}\\\\\phi_0=\frac{hc}{\lambda_0}=\frac{hc(2\lambda_2-\lambda_1)}{\lambda_1\lambda_2}

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