EXPERIMENTAL STUDY OF THE PHOTOELECTRIC EFFECT AND ITS RESULT: -

The experimental arrangement to study the photoelectric effect is shown in the figure. The ultraviolet rays entering quartz window are
incident on the photo-sensitive surface S, known as cathode. Collector C is kept at different positive or negative voltage with respect to S.
The photoelectric effect can be studied with reference to the frequency and intensity of the incident light, number of photoelectrons emitted and their maximum energy.
When proper positive potential is applied to collector C, all the  photoelectrons are attracted towards it and the maximum current recorded by the micro-ammeter gives an idea of the number of photo electrons.
When negative potential is applied to the collector, only such electrons which have sufficient energy to overcome the negative potential may reach the collector. On making collector more negative, photoelectric current decreases and becomes zero at or lower than some specific negative potential. This minimum negative potential of the collector with respect to the photosensitive surface at which photoelectric current becomes zero is called stopping potential.
According to the definition of stopping potential, electron on the surface of the photosensitive
surface having maximum velocity, v max , just reaches the collector plate overcoming stopping
potential V0. In the process, the work eV0 done by it is at the cost of its kinetic energy, 

( 1 / 2 ) m v2 max.

The graphs of photoelectric current versus the potential of collector with respect to the emitter for different intensities and frequencies of incident light are shown in the figure. It can be seen from the figure that for a given intensity, stopping potential depends on frequency and is thus independent of intensity of light. Also, for a given frequency, maximum saturation current depends on the intensity of light and is thus independent of its frequency.

1 ) The maximum energy of photo-electron depends on the frequency of incident light and not on its intensity.
( 2 ) The number of photo-electrons increases with increase in intensity of incident light.
( 3 ) The phenomenon of photo-emission is instantaneous. Within

10- 9 s, after light is incident, photo-electrons are emitted. The graph of stopping potential versus frequency is shown in the figure. This graph is linear.

PHOTOELECTRIC EFFECT AND WAVE THEORY OF LIGHT: -
Infact Wave theory fails to explain the characteristics of photoelectric effect.
( 1 ) According to the wave theory, energy and intensity of light wave depend on its amplitude. Hence energy of photo-electrons should increase with intensity of light. But experimental results indicate that the energy of photo-electrons does not depend upon the intensity of light.
( 2 ) According to the wave theory, energy of light has no relation with its frequency. Hence, change in energy of photo-electrons with the change in frequency cannot be explained.
( 3 ) Photo-electrons are emitted spontaneously. This cannot be explained by wave theory. Free electron in a metal is emitted only when it gets certain minimum energy called “work function” ( f ) of the metal. If the light has wave nature, free electron in metal may get energy gradually and some time elapses before it gets energy equal to its work function and gets emitted. This is in contradiction to the spontaneous emission.
( 4 ) With less intense light, the emission of electrons will be slower as per the wave theory. But with light of sufficiently high frequency, emission of photo-electrons is immediate even if its intensity is low.
EINSTEIN'S EXPLANATION: -

 In 1905, Einstein explained photo-electric effect using Planck’s hypothesis.
Planck had assumed that the emission of radiant energy occurs as photons, but after emission it transmits as a wave. Einstein assumed that emission, transmission and absorption of light take place in the form of photons.
According to Einstein, when light in the form of photon is incident on a metal, it is totally absorbed or does not lose its energy at all. The electron which receives hf amount of energy of photon spends energy equal to its binding energy and gets immediately emitted with the remaining energy.  

Thus, eV0 = (1/2) m v2 max  = hf - f = hf - hf0

That is V0 = (h / e) (f – f 0) 

According to this equation, the graph of V0 versus f ( as shown on the previous page ) is a straight line with slope h / e and intercept on X-axis, f0. Thus, experimental plot of the graph of ‘V0 versus f’ could be satisfactorily explained by Einstein for which Einstein got a Nobel prize.
The intensity of light incident on the metal surface is the amount of light energy incident per second per unit area normal to the surface. According to the photon theory of light, intensity of light I   = nhf, where, n = number of photons incident per second per unit area and hf = energy of photon of light of frequency f. Thus, according to the photon theory, more the intensity of light, more is the number of
photons incident per second. Hence, more photo-electrons are emitted and the current increases with intensity. Thus, photo-electric effect could be satisfactorily explained with the photon theory.