Effect of potential difference on the photoelectric current

Effect of potential difference on the photoelectric current

For a given metallic surface C, keeping the intensity (I₁) and frequency of the incident radiation constant, the effect of potential difference between the plates on the photoelectric current can be studied. Fig  shows the variation of photo electric current with the potential difference V between the two plates. When the positive potential of A is increased, the photoelectric current is also increased. However, if the positive potential is further increased such that it is large enough to collect all the photo electrons emitted from the plate C, the photoelectric current reaches a certain maximum value and this current is known as saturation current. If the potential of the plate A is made negative, the photocurrent does not immediately drop to zero but flows in the same direction as for positive potential. This shows that the photo electrons are emitted from the plate C with finite velocity. If the negative or retarding potential is further increased, the photo current decreases and finally becomes zero at a particular value. Thus, the minimum negative (retarding) potential given to the anode for which the photo electric current becomes zero is called the cut-off or stopping potential.

If m is the mass of the photo electron emitted with a velocity v_max then the kinetic energy associated with it is ½ mv²_max.

Since at the stopping potential V_o, the fastest electron is just prevented from reaching the plate A, workdone in bringing the fastest electron to rest = kinetic energy of the fastest electron. Since at the stopping potential V_o, the fastest electron is just prevented from reaching the plate A, workdone in bringing the fastest electron to rest = kinetic energy of the fastest electron.

eV_o = ½ mv²_max

The above equation indicates that the stopping potential depends upon the velocity of the fastest electron.

The experiment is repeated with the incident radiation of same frequency, but of higher intensities I₂ and I₃. It is found from the graph, the saturation currents are proportional to the intensities of the radiation. But, the stopping potential remains the same for all the intensities. Thus, for a given frequency of incident radiation, the stopping potential is independent of its intensity.