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 then `lambda`. Find the number of photoelectrons emitted before the emission of photo electrons stops.

Explanation

`(hc)/(lambda) =(hc)/(lambda_(0)) +eV_(s)`
`V_(s) =(hc)/(e) ((1)/(lambda) - (1)/(lambda_(0)))`
As electrons ejected, sphere becomes positively charged, its potential increases. A state is reached when electric potential of sphere equals stopping potential then emission stop. Let charge on sphere be q.
`V =(1)/(4pi epsilon_(0))(q)/(q) =V_(s)`
`(1)/(4pi in_(0)).(n e)/(a) = (hc)/(e) ((1)/(lambda) - (1)/(lambda_(0)))`
`n= (4pi in_(0) ahc)/(e^(2)) ((1)/(lambda) - (1)/(lambda_(0)))`
where n: number of photoelectrons emitted.