Electron Emission and Photoelectric Effect

• The phenomenon of emission of electrons from the surface of a metal is called electron emission.

• Work function − A certain minimum amount of energy is required to be given to an electron to pull it out from the surface of the metal. This minimum energy required by an electron to escape from the metal surface is called the work function of the metal.

• The minimum energy required for the electron emission from the metal surface can be supplied to the free electrons by any one of the following physical processes:

  • Thermionic emission − By suitable heating, sufficient thermal energy can be imparted to the free electrons to enable them to come out of the metal.

  • Field emission − By applying a very strong electric field to a metal, electrons can be pulled out of the metal.

  • Photoelectric emission − When light of suitable frequency illuminates a metal surface, electrons are emitted from the metal surface.

Photoelectric Effect

• The apparatus consists of an evacuated glass or quartz tube, which encloses a photosensitive plate C and a metal plate A.

• The window W will allow the light of a particular wavelength to pass through it.

• When a monochromatic radiation of suitable frequency obtained from source S falls on the photosensitive plate C, the photoelectrons are emitted from C, which get accelerated towards the plate A(kept at positive potential).

• These electrons flow in the outer circuit, resulting in the photoelectric current. Due to this, the microammeter shows a deflection.

• Factors affecting photoelectric current:

  • Effect of intensity of light on photocurrent − The number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.
    

  • Effect of potential on photoelectric current

• • Keep plate A at some positive accelerating potential with respect to plate C and illuminate plate Cwith light of fixed frequency ν and fixed intensity I₁.
    It is found that photoelectric current increases with increase in accelerating potential. At some stage, for a certain positive potential of plate A, all the emitted electrons are collected by plate Aand the photoelectric current becomes maximum or saturates. This maximum value of photoelectric current is called saturation current.
    The minimum negative potential V₀ given to plate A with respect to plate C at which the photoelectric current becomes zero is called stopping potential or cut off potential. If e is the charge on the photoelectron, then
    
    Where,
    m = Mass of photoelectron
    v_max = Maximum velocity of emitted photoelectron

  • Effect of frequency of the incident radiation − Taking radiations of different frequencies but of same intensity, the variation between photoelectric current and potential of plate A is obtained and shown in graph given below.

From the graph, we note:

(i) The value of stopping potential is different for radiation of different frequency.

(ii) The value of stopping potential is more negative for radiation of higher incident frequency.

(iii) The value of saturation current depends on the intensity of incident radiation, but is independent of the frequency of the incident radiation.

• Graph between stopping potential and the frequency of the incident radiation:

From the graph, we note:

(i) For a given photosensitive material, the stopping potential varies linearly with the frequency of the incident radiation.

(ii) For a given photosensitive material, there is a certain minimum cut-off frequency ν₀ (called threshold frequency), for which the stopping potential is zero.

• Laws of photo-electric emission:

  • For a given metal and frequency of incident radiation, the number of photoelectrons ejected per second is directly proportional to the intensity of the incident light.

  • For a given metal, there exists a certain minimum frequency of the incident radiation below which no emission of photoelectrons takes place. This frequency is called threshold frequency.

  • Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron is independent of the intensity of the incident light, but depends only upon the frequency (or wavelength) of the incident light.

  • The photoelectric emission is an instantaneous process.