The Photoelectric Effect

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There are three ways in which electrons eject out of a material. They are

(i) Thermionic emission

(ii) Field emission

(iii) Photo electric emission

In all the above cases, energy is given to the material but in different forms. If given in the form of heat it is called as Thermionic emission, if in the form of electrical energy, it is field emission and if in the form of light (photons), then it is photoelectric effect.

What is photoelectric effect?

When light of sufficiently small wavelength is incident on a metal surface, electrons are ejected from the metal. This phenomenon is called as 'photoelectric effect' and the ejected electrons are called as 'photoelectrons'. A systematic study of this effect can be done using the following experiment

Experimental study

Two metal plates are sealed in a vacuum tube. If light of reasonably short wavelength is made to fall on the plate (emitter). If a high potential, difference is applied to the plates, making the emitter negative and the collector positive a photocurrent is registered in the ammeter connected in series in the circuit as long as the emitter is irradiated with light.

Let us increase the potential difference between the plates continuously. We find that the photocurrent also increases but reaches a saturation. This shows that the number of electrons attracted by the collector is becoming more because of higher potential difference. After a certain potential, the number of electrons reaching the collector remains the same irrespective of the attracting potential. This must be due to the fact that the number of electrons ejected out remains the same and all the ejected electrons are attracted by the collector thereby producing a 'saturation region'.

The adjacent graph (V-I) shows the above observation. Now if the potential difference between the plates is made zero still there is a photocurrent, as shown by the intercept on the y-axis.

If the potential of the collector is made negative with respect to the cathode. Even then, a photocurrent is registered and if the negative potential is increased, the photocurrent decreases. For some negative potential of the collector, the photocurrent becomes zero and it is called as 'stopping potential'.

The above can be explained as follows. When the collector potential is negative, the electrons are repelled by the anode. Some electrons go back to the anode. Some of them with high kinetic energy are still able to reach the anode (collector). As the negative potential increase, less and less electrons reach the collector and finally when none can reach the photocurrent becomes zero.

The stopping potential is related to the maximum kinetic energy of the ejected electrons. The fastest photoelectron as it reaches the anode has kinetic energy given by

[K.E_max - eV₀] ..... (1)

where K.E_max - energy of the electron when it leaves the emitter.

eV₀ - increase in the potential energy of the electron as it moves from emitter to collector.

If the intensity of the light increases the photocurrent also increases proportionally but the stopping potential remains the same. This is depicted in the graph.

At the same time, if we decrease the intensity of light the amount of the photocurrent decreases but for even the weakest signal 'photoelectric phenomenon' takes place.

If classical theory is true, the lesser the intensity the energy imparted to the electron must be less and hence there should have been a 'threshold intensity' below which there is no photoelectric effect. But this is not true.

Instead, it was found that the frequency of the light is the key parameter. When the frequency of light is increased, the stopping potential also increases and there lies a threshold frequency below which there is no photoelectric effect.

The correct explanation for photoelectric effect was given by Albert Einstein in 1905. Einstein postulated that a beam of light consisted of small bundles of energy called as photons. The energy 'E' of the photon is proportional to the frequency ''u". Mathematically expressed as

E = hu ..... (2)

where 'h' is Planck's constant. The value of 'h' is 6.626 x 10^-34 Js. When a photon collides with an electron, it may transfer its energy to the electron. This transfer is an "all or none" process, the electron getting all the photon's energy or none at all. The energy received by the electrons helps it to escape from the surface of the metal and to do this the electron loses an amount of energy called as the work function of the surface of the metal (f). Therefore, if the energy received by the electron from photon is hu [equation (2)] and uses an energy (f) (work function of the surface) to escape the surface then the remaining is in the form of kinetic energy.

(K.E)_max + (f) = hu ..... (3) this is called as Einstein's photoelectric equation.

But the stopping potential V₀ provides a direct measurement of the maximum kinetic energy with which electrons leave the cathode.

Equation (3) can be written as

eV₀ = hu - f

The graph shows the variation of stopping potential with frequency in accordance to the above equation.

The above experimental study can be summarized as follows:

Before that, let us recollect some of the parameters and their symbols.

V₀ - Stopping potential

u₀ - Threshold potential

f - Work function

h - Planck's constant

u - Frequency of the incident light

e - Electronic charge

(i) The metal emits electrons when light of sufficiently small wavelength falls on it and the emission is instantaneous.

(ii) There exists a threshold frequency g₀ for a given metal, below which there is no photoelectric effect.

(iii) The photocurrent can be made zero by applying a negative potential to the collector and the minimum negative potential to produce zero photocurrent is called as stopping potential

(iv) The stopping potential depends on the frequency of the light falling on the metal and not on the intensity of light.

(v) The photocurrent increases with the intensity of the incident light.

Millikan made the first accurate measurement of cut-off voltage for sodium metal by using monochromatic light of known frequencies.