Describe an experiment to study photo-electric effect.
The experimental set up to study photoelectric effect is shown in Figure :
It consists of a highly evacuated tube having two electrodes 'A' and 'C'. The electrode 'C' is a photo-sensitive emitter which emits photoelectrons when exposed to ultra-violet radiation. The electrode 'A' is a charge (or electrons) collecting plate. The tube has a side window made of quartz covered with a filter through which the incident light of desired wavelength enters the tube and falls on the photo-sensitive plate 'C'.
Electrodes 'A' and 'C' are connected to a battery through a suitable reversing switch 'S'. Electrode 'A' can be brought to a positive or a negative potential with respect to electrode 'C' with the help of this switch.
Procedure : Electrons are emitted when ultraviolet radiations are made to fall on photo-sensitive plate 'C'. These electrons get attracted towards electrode 'A' when it is at a positive potential with respect to electrode 'C'. The flow of electrons from electrode 'C' to electrode 'A' makes electric current to flow in the circuit. This electric current is known as photoelectric current.
The photoelectric current is measured with a micro-ammeter ($\mu$A) connected in series. The potential difference between plates 'A' and 'C' is measured with the help of voltmeter (V).
Effect of Intensity of Incident Light on the Photoelectric Current
Photoelectric current (number of photoelectrons per second) is directly proportional to the intensity of the incident radiations, provided the frequency of incident radiations is greater than the threshold frequency.
As the intensity of the incident light increases (keeping the frequency constant), more and more photoelectrons are emitted by the electrode 'C' and hence photoelectric current increases linearly, that is, photoelectric current ($I_p$) is directly proportional to the intensity (I) of incident light.
Note :
1. Photoelectric current depends upon the intensity of incident light, provided frequency of incident light is greater than threshold frequency.
2. No photo electron is emitted if the frequency of incident light is less than the threshold frequency whatever the intensity of incident light may be.
Effect of Potential Difference on Photoelectric Current :
When light of suitable frequency (greater than the threshold frequency) falls on the photo-sensitive electrode 'C', photoelectrons are emitted. These electrons get accelerated towards the current collecting plate or anode 'A' which is at a given positive potential with respect to the electrode 'C'. They give rise to the photoelectric current. For a given frequency and intensity of incident light, the photoelectric current increases with the increase in applied positive potential (or voltage) of plate 'A'. When all the photoelectrons emitted by electrode 'C' reach the plate 'A', the photoelectric current has the maximum value which is called the saturation current. Saturation current will not increase with further increase in positive potential of plate 'A' because number of photoelectrons emitted is equal to the number of photoelectrons reaching the plate 'A'. Now, when potential of plate 'A' is decreased such that it attains negative potential with respect to electrode 'C', then photoelectric current decreases. The negative potential applied to plate 'A' is increased to a certain value $V_0$ for which photoelectric current becomes zero.
Thus , This minimum negative potential $V_0$ applied to plate or anode 'A' for which photoelectric current becomes zero is called cut-off potential or stopping potential.
At this stage, the maximum kinetic energy $\frac{1}{2}mv_{0}^2$ of photo electron must be equal to the energy acquired by an electron while passing through a potential difference $V_0$.
That is,
$\frac{1}{2}mv_{0}^2 = eV_{0}$
or
$K.E_{0} = \frac{1}{2}mv_{0}^2 = eV_0 \quad \dots (1)$
$K.E_{0} \propto V_{0}$
Thus, the maximum kinetic energy of a photoelectron can be determined by knowing the value of the stopping potential. Variation of photoelectric current with varying potential of plate A is shown in figure.
If the intensity of the incident light is increased (say from $I_1$ to $I_2$ and frequency is kept same, then the variation of the photo-electric current with the potential of the plate A is shown in figure 16. The values of photoelectric current and the saturation current are higher at high intensity of light than at low intensity of light but stopping potential is the same in both the cases.
Conclusion :
(i) Saturation of photoelectric current depends upon the intensity of the incident radiation, provided frequency of incident radiation is greater than the threshold frequency for the substance.
(ii) For a given beam of incident radiation, the intensity of incident radiation does not affect the stopping potential. That is, stopping potential does not depend upon the intensity of light.
(iii) Maximum kinetic energy of emitted photoelectrons does not depend upon intensity of incident radiation.
(iv) Emitted photoelectrons may have different kinetic energies.
There is energy distribution of electrons. Electrons revolving in different orbits in an atom have different force of attraction with their parent nucleus. Thus, different amount of energy is needed to emit these electrons.
Effect of Frequency of Incident Light on Photoelectric Current :
To study the effect of frequency of the incident light on the photoelectric current the intensity of incident light is kept constant but the frequency of incident light is changed so that in each case the saturation current is exactly the same.
Now for a given frequency ($\nu_1$) of the incident light, the positive potential at plate A is decreased to zero. It is found that the photo-electric current decreases. Now, the plate A is given negative potential which is increased till the photoelectric current becomes zero. Let this value of negative potential be $V_{01}$.
The experiment is repeated with the incident light of same intensity but of frequency $\nu_2 > \nu_1$. It is found that now, the stopping potential is higher than $V_{01}$. Let it be $V_{02}$
Conclusions: Thus, we find that (i) the value of stopping potential depends upon the frequency of the incident light (provided frequency is greater than the threshold frequency $\nu_0$). That is, stopping potential is directly proportional to the frequency of the incident light.
Thus,
$V_0 \propto \nu \quad (\text{for } \nu > \nu_0) \quad \dots (2)$
(ii) Value of saturation current does not depend upon the frequency of the incident radiation.
Note : Ratio of stopping potentials for frequencies $\nu_1$ and $\nu_2$ is given by,
$\frac{V_{02}}{V_{01}} = \frac{\nu_2}{\nu_1}$
Graph for Frequency and Stopping Potential :
When a graph is plotted between the frequency of the incident light and the stopping potential, it is found to be a straight line not passing through the origin. Figure shows graph between frequency of incident light and the stopping potential for two different emitting materials P and Q.
It shows that there is a minimum value of frequency known as threshold frequency or cut-off frequency $\nu_0$ of the incident light below which photoelectric emission is not possible.
The value of threshold frequency depends upon the nature of the substance or material emitting the photoelectrons.
Conclusions drawn from the graph :
(i) There is some least cut off frequency or threshold frequency $\nu_0$ for which stopping potential $V_0$ is zero. It implies that no photo emission is possible below cut off frequency even if the intensity of incident radiation is high.
(ii) Threshold frequency will be more for materials having higher work function.
(iii) Stopping potential $V_0$ varies linearly with the incident radiation frequency. The maximum kinetic energy of photoelectrons varies linearly with incident radiation frequency irrespective of its intensity.
Laws of Photoelectric Emission :
Law 1. For a given substance, there is a minimum frequency ($\nu_0$) below which no photoelectric emission takes place, whatever the intensity of incident light may be. For every substance, the value of threshold frequency is different.
Law 2. The number of photoelectrons emitted per second (i.e. photoelectric current) by a substance is directly proportional to the intensity of incident light, provided the frequency of the incident light is greater than the threshold frequency.
Law 3. The maximum kinetic energy of the photo-electrons increases with the increase in the frequency of the incident light, provided the frequency of incident light is greater than the threshold frequency. The maximum kinetic energy of the emitted photoelectrons is independent of the intensity of the incident light.
Law 4. The process of photoelectric emission is instantaneous. As soon as light of suitable frequency (more than threshold frequency) is incident on a substance, photo-electrons are emitted without any significant time lag between emission of photo electrons and the incidence of radiation is just $10^{-9}$s.