Stopping potential  of photo electric effect

                                The relation between current and applied voltage illustrates the nature of the photoelectric effect. For discussion, a light source illuminates a plate P, and another plate electrode Q collects any emitted electrons. We vary the potential between P and Q and measure the current flowing in the external circuit between the two plates.

If the frequency and the intensity of the incident radiation are fixed, the photoelectric current increases gradually with an increase in positive potential on collector electrode until all the photoelectrons emitted are collected. The photoelectric current attains a saturation value and does not increase further for any increase in the positive potential. The saturation current depends on the intensity of illumination, but not its wavelength.

If we apply a negative potential to plate Q with respect to plate P and gradually increase it, the photoelectric current decreases until it is zero, at a certain negative potential on plate Q. The minimum negative potential given to plate Q at which the photoelectric current becomes zero is called stopping potential or cut off potential.

i. For the given frequency of incident radiation, the stopping potential is independent of its intensity.

ii. For a given frequency of the incident radiation, the stopping potential Vo is related to the maximum kinetic energy of the photoelectron that is just stopped from reaching plate Q. If  is the mass and  is the maximum velocity of photoelectron emitted, then

If q_e is the charge on the electron and  is the stopping potential, then the work done by the retarding potential in stopping the electron , which gives

The above relation shows that the maximum velocity of the emitted photoelectron is independent of the intensity of the incident light. Hence,

The stopping voltage varies linearly with frequency of light, but depends on the type of material. For any particular material, there is a threshold frequency that must be exceeded, independent of light intensity, to observe any electron emission.