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A monochromatic light of wavelength lam...

A monochromatic light of wavelength ` lambda` is incident on an isolated metallic sphere of radius a. The threshold wavelength is ` lambda_0` which is larger than ` lambda`. Find the number of photoelectrons emitted before the emission of photoelectrons will stop.

Text Solution

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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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