18.2 Photoelectric Effect

18.2 Photoelectric Effect

The process of emission of electrons from a metal surface when exposed to light of suitable frequency or wavelength is called the photoelectric effect. The emitted electrons are known as photoelectrons. The photoelectric effect is demonstrated by the apparatus shown in Fig. 18.1. An evacuated glass tube X contains two electrodes. The electrode B connected to the positive terminal of the battery acts as anode. The metal electrode C connected to negative terminal acts as cathode. When monochromatic light of suitable frequency is allowed to shine on cathode, it begins to emit electrons. These photoelectrons are attracted by the positive anode and the resulting current is measured by a micro-ammeter. The current stops when light is cut off, which proves that the current flows because of incident light. This current is, hence, called photoelectric current.

(Fig. 18.1: Experimental arrangement to observe photoelectric effect.)

The maximum energy of the photoelectrons can be determined by reversing the connections of the battery in the circuit i.e., now the anode A is negative and cathode C is at positive potential. In this condition, the photoelectrons are repelled by the anode and the photoelectric current decreases. If this potential is made more and more negative, at a certain value, called stopping potential $V_{o}$, the current becomes zero. Even the electrons of maximum energy are not able to reach collector plate. The maximum kinetic energy of photoelectrons is, thus

where $m$ is mass, $v$ is velocity and $e$ is the charge on electron. If the experiment is repeated with light beam of higher intensity, the amount of current increases but the current stops for the same value of $V_{o}$. Figure 18.2 shows two curves of photoelectric current as a function of potential $V$ where $I_{2} > I_{1}$. However, if the intensity is kept constant and experiment is performed with different frequencies of incident light, we obtain the curves as shown in Fig. 18.3. The current is same but stopping potential is different for each frequency of incident light, which indicates the proportionality of maximum kinetic energy with frequency of light $f$.

(Fig. 18.2: Characteristic curves of photocurrent vs. applied voltage for two intensities of monochromatic light.)

(Fig. 18.3: Characteristic curves of photocurrent vs applied voltage for light of different frequencies.)

The important results as indicated by the graph between $(K.E.)_{\max}$ and frequency of incident light of the experiments are:

1. The electrons are emitted with different energies. The maximum energy of photoelectrons depends on the particular metal surface and the frequency of incident light.
2. There is a minimum frequency called threshold frequency below which no electrons are emitted, however, intense the light may be. For example, blue light produces photoelectric emission in sodium metal but red light does not (Fig. 18.4). This threshold frequency $f_{o}$ varies from metal to metal. The corresponding wavelength of incident light is called threshold wavelength.

(18.4: Red and blue light incident on sodium metal)

3. Electrons are emitted instantaneously; the intensity of light determines only their number.

These results could not be explained on the basis of electromagnetic wave theory of light. According to this theory, increasing the intensity of incident light should increase the K.E. of emitted electrons which contradicts the experimental result. The classical theory cannot also explain the threshold frequency of light. According to this theory, even the light of lesser energy should eventually transfer enough energy to liberate electrons. But this does not happen.