Photoelectric Effect and It’s laws

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Photoelectric Effect :-

When light falls on the metal surface, Some electrons near the metal surface absorb enough energy from the incident radiation to overcome the attraction of the positive ions in the material of the surface. After gaining sufficient energy from the incident light, the electrons escape from the surface of the metal into the surrounding space, this phenomenon is called photoelectric effect.

The phenomenon of photoelectric emission was discovered by Heinrich Hertz in 1887

Experimental study of photoelectric effect :-

Fig 1 :- Experimental arrangement for study of photoelectric effect.

The figure consists on an evacuated glass/quartz tube having a photosensitive plate C and another metal plate A. Monochromatic light from the source S of sufficiently short wavelength passes through the window and falls on the plate C

The electrons are emitted by the plate C and are collected by the plate A through the electric field created by the battery.

  • The battery maintains in the potential differences between the plates C and A that can be varied.
  • The polarity of the plate C & A can be reversed by commutator.

Thus, the plate A can be maintained at a desired positive or negative potential with respect to the emitter C, the electrons are attracted to it. The emission of electrons causes flow of electric current in the circuit.

  • The potential difference between the emitter and collector plates is measured by a voltmeter (V) whereas the resulting photocurrent flowing circuit is measured by a microammeter (μA).

Laws of photoelectric effect :-

  1. For a given photosensitive material and frequency of incident radiation (above the threshold frequency), the photoelectric current is directly proportional to the intensity of incident light.
  2. For a given photosensitive material, the exists a certain minimum cut-off frequency of the incident radiation called the threshold frequency. Above the threshold frequency, the stopping potential or equivalently the maximum kinetic energy of the emitted photoelectrons increases linearly with the frequency of the incident radiation, but is independent of its intensity.
  3. The photoelectric emission is an instantaneous process without any time (10⁻⁹ or less), even when the incident radiation is made exceedingly dim.

Effect of intensity of light on Photoelectric current :-

The Collector A is maintained at a positive potential with respect to emitter C are attracted towards collector A. Keeping the frequency of the incident radiation and the accelerating potential fixed, the intensity of light is varied and the resulting photoelectric current is measured each time.

Fig 2 :- Experimental arrangement for study photoelectric effect.
  • It is found that the photocurrent increases linearly with intensity of incident light. The photocurrent is directly proportional to the number of photoelectrons are emitted per second. This implies that the number of photoelectrons emitted per second directly proportional to the intensity of incident radiation.

Effect of potential on photoelectric current :-

We keep the plate A at some positive accelerating potential with respect to the plate C and illuminated the plate C with light of fix frequency ‘v’ and fixed intensity I₁ . We next vary the positive potential of plate A gradually and measure the resulting photoelectric current each time.

It is found that the photoelectric current increases with increase in accelerating (positive) potential.

  • At some stage for a certain positive potential of a plate A. All the emitted electrons are collected by the plate A and the photoelectric current becomes maximum or saturates.

We now apply a negative (retarding) potential to the plate A with respect to the plate C and make it increasingly negative gradually.

Fig. 3 :- Variation of photocurrent with Collector Plate potential for different intensity of incident radiation.
  • When the polarity is reversed the electrons are repelled and only the most energetic electrons are able to reach collector A.

The photoelectric current is found to decrease rapidly it drops to zero at a certain sharply defined. Critical value of the negative potential V₀ on the plate A.

  • For a particular frequency of incident radiation, the minimum negative potential V₀ given to the palate A for which the photoelectric current stops or becomes zero is called the cut-off of stopping potential.
  • Photoelectric current is zero when the stopping potential is sufficient to repel even the most energetic photoelectrons with the maximum kinetic energy (K) so that

K = e V₀

Effect of frequency on incident radiation on stopping potential :-

Fig. 4 :-

We suitably adjust the same intensity of light radiation at various frequencies and study the variation of photoelectric current without Collector Plate potential.

We obtain different values of stopping potential but same value of the saturation current for incident radiation of different frequencies.

  • The energy of the emitted electrons depends on the frequency of the incident radiations.

The stopping potential is more negative for higher frequencies of incident radiation.

  • In the above figure the stopping potentials are in the order V₀₃ > V₀₂ > V₀₁ if the frequencies are in the order v₃ > v₂ > v₁ .

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