Photo electric effect
Consider a negativity charged zinc plate connected to a gold leaf electroscope (Fig. 1). The divergence in the leaves indicates the potential of the plate. Let a beam of ultraviolet light be incident in this plate. It is observed that the divergence decreases gradually. This is due to the ejection of electrons from the plate.
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| Fig. 1. Ejection of electrons from surface of metal by light. |
Definition:
"Photo electric effect is the phenomenon of emission of electrons from the surfaces of certain substances, mainly metals, when light of shorter wavelength is incident upon them."
Experiment study of photo electric effect
The apparatus required for the experimental study of photo electric effect is shown in Fig. 2. It consists of an evacuated glass tube 'T' fitted with two electrodes. Electrodes 'E' known as emitter is coated with a photo sensitive material. Light from a source 'S' after passing through a quartz window 'W' is made to fall upon 'E'. Collecting electrodes can be provided with a potential whose value can be changed with the help of a potentiometer 'P' fed with a 10 volt battery through a reversing key 'R'. Key 'R' enables us to provide both positive and negative potential to the collecting electrodes. Potential difference between two electrodes is noted with a voltmeter while the current is given by the ammeter 'A'.
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| Fig. 2. Experimental setup for the study of photo electric effect. |
(a) Effect of collector's potential on photo electric current. Keeping the intensity and frequency of light from 'S' fixed, note the value of current in the circuit by changing potential of collector from positive to zero and to negative value. Plot a graph between the potential (along X-axis) and photo electric current (along Y-axis). Two such curves, one for low intensity (i) and second foe high intensity (ii) are shown in Fig. 3.
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| Fig. 3. Variation of photo electric current due to potential of anode. |
Each curve shows that the current changes continuously with a change in potential. Beyond some positive potential of collector the current attains a saturation value while for a certain negative value 'V₀' it is required to zero. 'V₀' is called the stopping potential. Following conclusions can be drawn from above observations :
(i) Presence of current for zero value potential indicates that the electrons are ejected from the surface of emitter with some energy.
(ii) A gradual change in the number of electrons reaching the collector due to change in its potential indicates that the electrons are ejected with a variety of velocities.
(iii) Current is reduced to zero for some negative potential of collector indicating that there is some upper limit to the energy of electrons emitted.
(iv) For any potential of collector the current in case of curve (ii) is greater than that in case (i). This means the current depends upon the intensity of incident light.
(v) Both the curves meet at same point on X-axis indicting that stopping potential in independent of the intensity of light.
(b) Effect of intensity of light. Keeping potential of collector fixed note the value of current in the circuit for different intensity of light. A graph between intensity of light and photo electric current is found to be a straight line (Fig. 4) indicating that the photo electric current is directly proportional to the intensity of incident radiation.
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| Fig. 4. Intensity of light. |
(c) Effect of frequency of light. Repeat the experiment as described in case (a) for different sources of frequencies f₁, f₂, f₃, giving same intensity of light. Three curves (i), (ii) and (iii) as shown in Fig. 5 are obtained. The curves shows that :
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| Fig. 5. Variation of current with anode potential for different frequencies. |
(i) Stopping potential depends upon the frequency of light. Greater the frequency of light, greater is the stopping potential.
(ii) Saturation current is independent of frequency. Note the value of stopping potentials V₀₁, V₀₂, V₀₃, ......., for various frequencies f₁, f₂, f, ....... respectively. A straight line as shown in Fig. 6 is obtained the straight line has an intercept 'f₀' on f-axis indicating that for frequency 'f₀' there will be no current when collector is at zero potential. This is the minimum frequency capable of producing photo electric effect and is called threshold frequency. Greater the frequency of incident light, greater the value of negative potential required to stop the current. Hence, maximum energy of the emitted electrons depends upon the frequency of light.
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| Fig. 6. Variation of stopping potential with frequency. |
Law of photo electricity
The conclusions drawn from the experimental study of photo electric effect can be summed up as laws of Photoelectricity.
(i) Photo electric effect is an instantaneous process.
(ii) Photo electric current is directly proportional to the intensity of incident light and is independent of its frequency.
(iii) The stopping potential and hence the maximum velocity of the electrons depends upon the frequency of incident light and is independent of its intensity.
(iv) The emission of electrons stop below a certain minimum frequency known as threshold frequency.
Einstein's theory of photo electric effect
Einstein explained photo electric effect on the basis of Planck's quantum theory. According to Max Planck's radiation was composed of energy bundles only on the neighborhood of the emitter. Einstein suggested that these energy bundles known as 'photons' preserve their identity throughout their life. Energy contained in bundle or packet is
E = hf
It is matter of common observation that the electrons are ejected only when light is incident on a metal. This is due to the existence of a potential barrier all around the surface of metal. The electron must possess certain minimum energy 'W₀' in order to cross the barrier, 'W₀' is known as work function. It is defined as the minimum energy required to pull an electron out from the surface of metal.
An incident photon supplies whole of its energy 'hf' to the electron, which consumes an energy 'W₀' against the work function and comes out with the remaining energy as its kinetic energy [Ek = ½ (mc²)].
½ mv²max = hf - W0 ... (1)
If 'f₀' is the shareholder frequency, the energy 'hf₀' of the photons will be just sufficient to help the electron in overcoming the potential barrier.
hf₀ = W₀ ...(2)
Substituting for 'W₀' in equation (1), we get
½ mv²max = hf - hf0
or ½ mv²max = h (f - f0) ....(3)Equation (3) is known as Einstein's equation of photo electric effect.
It is clear from equation (3) that greater the frequency of incident radiation, greater is the kinetic energy of the electron and hence greater negative potential is required to stop it.
An increase in intensity of light results in an increase in the number of photons which is turn results in ejection of more number of electrons. Hence, photo electric current is proportional to the intensity of light.
Electrons coming from the surface, spend energy only on overcoming the potential barrier. Therefore, kinetic energy of these electrons is maximum. The incident radiation penetrates the metal to thickness of about 10-6 cm. Thus, it will be able to eject the electrons lose some of the energy as they rise to the surface and hence are emitted with a lesser kinetic energy. Different electrons lose some amounts of energies. This is the reason that electrons are ejected with a variety of velocities.
If the frequency of incident radiation is less than 'f₀' given by equation (2), it is unable to help the electron in overcoming potential barrier. This is the reason for the existence of threshold frequency.
If V₀ = stopping potential
½ mv²max = eV0 ... (4)
From equation (1) and (2), we get
eV0 = hf - W0, V0 = (h/e) f - (W0/e)
Let h/e = A and W0/e = B
V0 = Af - B ...(5)
It is the equation of a straight line between f (along X-axis) and V₀ (along Y-axis) shown in Fig. 6
Calculation of f₀ (threshold frequency)
If V₀ = 0, from equation (5),
0 = Af - B
or f = B/A = W₀/e × e/h = W₀/h = f₀ [From equation (2)]
Thus, the intercept of 'V₀ - f' curve of f-axis gives the value of threshold frequency.
Calculation of 'W₀' (work function)
If f = 0, V₀ = V'
From equation (5) V' = - B = - W₀/e
W₀ = - eV' = e (- V')
or Work function = e × (intercept on V₀-axis)
Calculation of 'h'
Slope 'm' of straight line given by equation (5) us
m = A = h/e ∴ h = em
or Planck's constant = e × slope of 'V₀ - f' curve.
Photo electric cell
It consists of an evacuated bulb B, whose inside is coated with an alkali metal 'P', leaving a clear portion 'W' in the form of a window (Fig. 7). The bulb is made up of glass if it is to be used for white light and is made up of quartz if it is to be used in case of ultraviolet light. It has am electrode 'C' which is given a positive potential with the help of a battery. Light from a source 'S' is focussed into a metal P with the help of a convex lens 'L'. An ammeter connected in the circuit indicates the photo electric current.
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| Fig. 7. Photo electric cell. |
Application of photo electric cell
Photo electric cell has found a number of uses in various fields of science.
(i) It plays an important role in television studio. It converts light and shade of the picture into electrical waves which after a proper processing are transmitted to distant stations.
(ii) It is used for reproduction of sound in films. Microphone converts sound into electric waves which after amplification are fed to an electric lamp. Intensity of light from this lamp records lines of varying transparency on the film. During reproduction, a beam of light falls on a photo cell after crossing through this film. Photo cell converts light back into electrical oscillation which produces sound when fed to the receiver.
(iii) It is used for triggering fire alarm. In factories using chemical or explosive materials, photo cells are fitted at selected places. Light from any accidental fire falls on the cell. This produces a current which after amplification is fed to an alarm.
(iv) It is used in operating burglar's alarm. Ultraviolet light from a source is incident constantly on a cell. Any unwanted person entering a room cuts that beam unknowingly, thus stopping the current for a fraction of a second. This triggers an alarm.
(v) It is used for automatic switching of street light. Light from sun during day falls constantly on the cell making a current to flow through the circuit continuously. This current after amplification is fed to an electromagnet which keeps the key of the street light circuit open. In the evening, after sunset intensity of light and hence the current decreases. The electromagnet loses its strength. As a result of this the key is closed and the street light is automatically switched on.
(vi) A photo cell coupled with an electronic counter can be used to count automatically. The number of persons entering and leaving a hall. Each person will cut a beam of ultraviolet light once, thus producing a kick in the counter.
(vii) It is used to compare the illuminating power of the two sources. Current produced is directly proportional to intensity which I turns is proportional to the illuminating power of the source. Ratio of deflection in ammeter with two sources of light gives the ratio of their illuminating powers.
Keywords
1. Photo electric cell. Device which converts light into electricity.
2. Photo electric current. Current flowing in the circuit due to the emitted photo electrons.
3. Photo electric effect. Phenomenon of conversion of light into electricity.
4. Photo sensitive material. Material which emits electrons due to incidence of light.
5. Potential barrier. Electrostatic obstruction which restrict the outer orbital electrons to go away.
6. Quartz. Material which allows ultraviolet light to pass through it.
7. Stopping potential. Negative potential on the collector which reduce the photo electric current to zero.
8. Threshold frequency. Minimum frequency capable of producing photo electric effect.
9. Ultraviolet light. Light of wavelength just smaller than that of violet light.
10. Wavelength. Distance between two consecutive crestes or between two consecutive throughs.
11. Work function. Minimum energy required by an electron to overcome the potential barrier.
Key Formulae
Equation of photo electric effect
½ mv²max = hf - hf0
½ mv²max = h (f - f0)
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