(a)

a) It is not necessary that if the energy supplied to an electron is more than the work function it will come out. It comes out of the metal atom only when it absorbs a single photon with energy greater than or equal to the work function. The electron after receiving energy may loose its energy due collisions with other metal atoms. So most of them get scattered into the metal. Only a few electrons near the surface may come out of the surface of the metal for whom the incident energy is greater than the minimum threshold energy to loose an electron (work function) of the metal. So, it is not necessary that all the electrons that absorb a photon come out as photoelectrons irrespective of their location.

b) When the light source is brought near the photocell, the intensity of the light increases, which doesn’t effects the stopping potential but the photo-current increases, the following diagram justifies the above statements,

In the plot, I denotes the intensity of the light.