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A monochromatic light of wavelengthlambda is incident on a isolated metallic sphere of radius a. The threshol wavelength islambda_0 which is larger thanlambda. Find the number of photoelectrons emitted before the emission of photoelectrons will shop. |
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Answer» Solution : As the metallic sphere is isolated, it become POSITIVELY charged when electrons are ejected from it. There is an extra attractive force on the photoelectrons . If the potential of the sphere is raised to V, the electron should have a minimum energy `( varphi + eV)` to be able to COMES out. Thus, emission of photoelectrons will stop when ` (hc/ (lambda))= varphi + eV` ` = hc/ (lambda_0) + eV` or, `V= hc/e ((1/(lambda))-(1/(lambda_0))).` ` The charge on the sphere needed to take its potential ` to V is ` ` Q= (4 pi (epsilon_0)a) V.` ` The number of electrons emitted is, therefore, ` ` n= (Q/e)= (4 pi (epsilon_0)a V/ e)` ` (4 pi (epsilon _0) AHC /e^2)( 1/ lambda- (1/ lambda_0)).` |
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