In a photoelectric set-up a point source of light (of power $3.2\times {10}^{-3}W$  ) emits monoenergetic photons of energy 5.0eV. The source is located at a distance of 0.8m from the centre of a stationary metallic sphere of work function 3.0eV and of radius  $8.0\times {10}^{-3}m$ . The efficiency of photoelectric emission by the metallic sphere is one for every ${10}^6$  photons incident on it. Assume that the sphere is isolated and initially neutral and the photo electrons emitted by it are instantly swept away. As a result of it, the sphere gets positively charged and acquires a positive potential and after a certain time the photoelectron emission from it stops. Take the energy reaching the sphere from the source of light per second to be $E=\frac{{\mathrm{Pr}}^2}{4R^2}$  , where  r  is the radius of the sphere, R is the distance between the point source and the centre of the sphere and P is the power of the source.