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

Explanation

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)).`