Effect of Frequency and Intensity of Light in Photoelectric Effect

Effect of Frequency and Intensity of Light in Photoelectric Effect

The apparatus required for the experimental study of photoelectric effect as shown in figure. It consists of an evacuated glass tube ‘T’ fitted with two electrodes. Electrode ‘P’ known as emitter is coated with a photo-sensitive material. Light from a source, after passing through a quartz window ‘W’, is made to fall upon “P’. Collector C is kept at different positive or negative voltage with respect to P. 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,vmax , 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.

Effect of Collector’s Potential on Photoelectric Current

Photoelectric CurrentKeeping 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 photoelectric current (along Y-axis). Two such curves, one for low intensity (i) and second for high intensity (ii) are shown in figure.

Each curves shows that the current changescontinuously 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 reduced to zero. ‘V0’ is called the stopping potential. Following conclusions can be drawn from above observations:

(a) Presence of current for zero value potential indicates that the electrons are ejected from the surface of emitter with some energy.

(b) A gradual change in number of electrons reaching the collector due to change in its potential indicates that the electrons are ejected with a variety of  velocities.

(c) Current is reduced to zero for some negative potential of collector indicating that there is some upper limit to the energy of electrons emitted.

(d) For any potential of collector the current in case of curve (b) is greater than that in case (a). This means the current depends upon the intensity of incident light.

(e) Both the curves meet at same point on X-axis indicating that stopping potential is independent of the intensity of light. 

Current Intensity and Threshold Frequency

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 photoelectric current is found to be a straight line indicating that the photoelectric current is directly proportional to the intensity of incident radiation.

Effect of Frequency of Light
Graph Between Potential and Current

Repeat this experiment as described in case (a) for different sources of frequencies f1,f2,and f3 giving same intensity of light. Three curves (i), (ii) and (iii) as shown in figure are obtained. The curves show that:

(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 values of stopping potential V01, V02, V03,....., for various frequencies f1, f2, f3,... respectively. Plot a graph between frequency (f) and the stopping potential. A straight line as shown in figure is obtained. The straight line has an intercept ‘f0’ there will be no current when collector is at zero potential. This is the minimum frequency capable of producing photoelectric 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 electron depends upon the frequency of light.

Photoelectric Current

Area of Metal SurfaceLet P be the power of a point source of electromagnetic radiations, then intensity I at distance r from the source is given by 

I = P/4Ï€r2 (W/m2)

If A is the area of a metal surface on which radiations are incident, then the power received by the plate is

P' = IA = P/4Ï€r2 (W)

If f is the frequency of radiation, then the energy of photon is given by 

E = hf

The Variation of Frequency Versus Stopping PotentialThe number of photons incident on the plate per second (called photon flux) is given by

Φ  = P' / E = [P/4Ï€r2 × A / hf]

If f > f0 (threshold frequency) and photon efficiency of the metal plate is η%, then the number of photoelectrons emitted per second is given by

n = Φη/100 [P/4Ï€r2 × A / hf]] η/100

Finally, the photocurrent i is given