Photoelectric Effect

The wave nature of radiation suggests that energy is emitted or observed continuously as electromagnetic waves. However, wave nature of radiation cannot explain the experimentally observed phenomena like photoelectric effect, thermionic emission etc. Max Planck gave the revolutionary theory, called Planck’s quantum theory about the nature of radiation. According to this theory, the radiant energy is emitted in packets and not continuously, each packet carries a certain amount of energy with the speed of light.

Photoelectric Effect

Whenever light or electromagnetic radiation fall on a metal surface, it emits electrons. This phenomenon of emission of an electron from a metallic surface when radiation of suitable frequency falls upon it is called photoelectric effect. These electrons are called photoelectrons.

Metals like Zinc, Cadmium etc are more sensitive only to ultraviolet rays whereas alkali metals like Sodium, Potassium etc are sensitive even to visible light.

Quantum Theory of Radiation

According to the quantum theory of radiation, the energy from the body is emitted in separate packets of energy each packet is called a quantum of energy. Each quantum carries a definite amount of energy called a photon. Therefore, the energy carried by each photon is given by:

$$E = hf \dots (i) $$

Where, f is the frequency of radiation and h is a Planck constant whose value is 6.62×10^-34 joule sec.

Experimental Study of Photo Electric Effect

The experimental setup consists of an evacuated glass or quartz tube with two electrodes A and C. A is a node and C are the cathodes. A constant potential difference is maintained between the cathode C and the anode A by a battery. The photoelectric current is measured by millimeter while the potential difference is measured by a voltmeter V. The tube is evacuated so that emitting surface is not contaminated by collisions with air molecules and electrons.

When a suitable radiation is an incident on the electrode C, electrons are emitted. These electrons get accelerated towards the plate A if it is kept at a positive potential with respect to the cathode. A current thus flows in the outer circuit which is called photo-current.

When intensity and frequency of the incident light are kept fixed while the potential of the anode is varied, it is increased in positive potential on the anode A till it reaches a value when photoelectric current reaches a saturation value. Here all the emitted electrons reach the anode A and there is no further increase in photocurrent with the increase in the positive potential of electrode A.

On the other hand, if the negative potential is applied to the plate A with respect to the cathode and is increased gradually, we find that photocurrent decreases rapidly and finally becomes zero at a certain negative potential on plate A. The minimum value of negative potential to plate A at which photoelectric current becomes zero is called stopping potential or cut off potential (V₀). In such a case, the work done by stopping potential is equal to the maximum kinetic energy of the photoelectrons emitted

$$\text {i.e.} \: eV_0 = \frac 12 m v_{max} ^2 $$

Effect of Intensity of Incident Light on the Photo Electric Current

Suppose a constant potential difference be applied across the electrode A and C. When ultra-violet light is incident on the cathode C, photoelectrons are emitted which are collected by plate A. The photoelectric current I_p constituted by these photoelectrons is measured by micro-ammeter. As the intensity of the incident light increases keeping frequency constant more photoelectrons are emitted by the electrode C and hence photoelectric current increases linearly I_p α I. The variation of photoelectric current with the intensity of incident light is shown in the figure. Since the photoelectric current is directly proportional to the number of photoelectrons emitted per second, therefore the number of photoelectrons emitted per second is directly proportional to the intensity of incident light.

Effect of Potential on Photoelectric Current

When the light of suitable frequency falls on the photosensitive electrode C, photoelectrons are emitted. These electrons get accelerated towards the electrode C and constitute the current called photoelectric current. For fixed frequency and incident of light, these photoelectric current increases with increase in applied positive potential of plate A. When all the photoelectrons emitted by electrode C reach the plate A, the photoelectric current attains maximum value known as saturation current. Now the potential of plate A is decreased such that it attains negative potential with respect to electrode C. The negative potential applied to plate A is increased to a certain value V₀ , for which no-photo-electrons reach the plate A for which photoelectric current becomes zero is called cut-off potential or stopping potential.

At this stage, the maximum kinetic energy \(\frac 12 mv_{max}^2 \) of photoelectron must be equal to \( eV_0\)

stopping potential is equal to the maximum kinetic energy of the photoelectrons emitted

$$\text {i.e.} \: \frac 12 m v_{max} ^2 = eV_0 $$

Thus, the maximum kinetic energy of a photoelectron can be determined by the knowing the value of the stopping potential.

If the intensity of the incident light is increased and frequency is kept same then the value of photoelectric current and saturated current increase but there is no change on stopping potential.

Effect of Frequency of Incident Light on stopping Potential

The intensity of incident light is kept constant, but the frequency is changed so that in each case the saturation current is exactly the same. Now for a given frequency f₁ of the incident light, the positive potential at plate A is decreased to zero. Now, the plate A is given negative potential be V₀₁. The experiment is repeated with the incident light of frequency f₂>f₁. It is found that stopping potential also increases. Thus, we found that the value of stopping potential depends on upon the frequency of the incident light.

Threshold frequency

When a graph is plotted between the frequency of the incident light and the stopping potential, it is found to be a straight line as shown in the figure. It shows that there is a minimum value of frequency f₀ of the incident light below which photoelectrons emission is not possible. This frequency is known as threshold frequency or cut-off frequency f₀. The value of threshold frequency depends on the nature of the substance emitting the photo-electrons.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, et al. Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.