Explain the effect of potential difference on photoelectric current.

Explanation

(i) To study the effect of potential difference V between the electrodes on photoelectric current, the frequency and intensity of the incident light are kept constant.
(ii) Initially the potential of A is kept positive with respect to C and the cathodeis irradiated with the given light.
(iii) Now, the potential of A is increased and the corresponding photocurrent is noted.
(iv) As the potential of A is increased, photocurrent is also increased. However a stage is reached where photocurrent reaches a saturation value ( saturation current ) at which all the photoelectrons from C are collected by A.
(v) This is represented by the flat portion of the graph between potential of A and photocurrent.
(vi) When a negative ( retarding ) potential is applied to A with respect to C, the current does not immediately drop to zero because the photoelectrons are emitted with some definite and different kinetic energies.
(vii) The kinetic energy of some of the photoelectrons is such that they could overcome the retarding electric field and reach the electrode A.
(viii) When the negative ( ratarding ) potential of A is gradually increased, the photocurrent starts to decrease because more and more photoelectrons are being repelled away from reaching the electrode A. The photocurrent becomes zero at a particular negative potential `V_(0)`, called stopping or cut-off potential.
(ix) Stopping potential is that the value of the negative (retarding ) potential given to the collecting electrode A whichis just sufficient to stop the most energetic photoelectrons emitted and make the photocurrent zero.
( x) At the stopping potential, even the most energetic electron is brought to rest. Therefore, the initial kinetic energy of the fastest electron `( K_("max"))` is equal to the work done by the stopping potential to stop it `( eV_(0))` .
`K_("max")= (1)/(2) mv_("max")^(2) = eV_(0)` .....(1)
(xi) Where `v_("max")` is the maximum speed of the emitted photoelectron.
`v_("max") = sqrt((2eV_(0))/( m))`
`v_("max")=sqrt((2 xx1.602 xx 10^(-19))/(9.1 xx 10^(-31))xxV_(0))`
`= 5.93 xx 10^(5) sqrt(V_(0))` ....(2)
From equation (1)
`K_("max") = eV_(0)` (in joule ( or ) .....(3)
`K_("max") = V_(0)` (in eV)
(xii) When the intensity of the incident light alone is increased ,the saturation current also increases but the value of `V_(0)` remains constant .
(xiii) Thus, for a given frequency of the incident light, the stopping potential is independent of intensity of the incident light. This also implies that the maximum kinetic energy of the photoelectrons is independent of intensity of the incident light.