State Einstein’s photoelectric equation.

Short Answer

Einstein’s photoelectric equation relates the energy of incident light to the kinetic energy of emitted electrons in the photoelectric effect. It is expressed as:

Where   is the maximum kinetic energy of the emitted electron,   is Planck’s constant,   is the frequency of light, and   is the work function of the metal. This equation explains why electrons are emitted only if light frequency exceeds a threshold frequency.

Detailed Explanation :

Einstein’s Photoelectric Equation

The photoelectric effect could not be explained by classical wave theory, which predicted that light intensity, rather than frequency, should determine electron emission. In 1905, Albert Einstein proposed that light consists of photons or quanta of energy, and that each photon transfers its energy to a single electron. Using this idea, he formulated the photoelectric equation:

  •  = maximum kinetic energy of the emitted electron
  •  = Planck’s constant ( Js)
  •  = frequency of incident light
  •  = work function of the metal, i.e., minimum energy required to release an electron

This equation demonstrates that electron emission depends on light frequency, not intensity, and predicts the threshold frequency ( ) below which no electrons are emitted, regardless of intensity.

Explanation of Terms

  1. Photon Energy ( )
    • Represents the energy carried by each photon of light.
    • Higher frequency light has more energetic photons.
  2. Work Function ( )
    • The minimum energy required for an electron to escape from the metal surface.
    • Different metals have different work functions.
  3. Kinetic Energy ( )
    • The leftover energy after an electron escapes.
    • It depends linearly on the frequency of incident light above threshold.

Graphical Representation

  • A graph of   vs.   shows a straight line:
    • Slope = Planck’s constant
    • Intercept =
  • Frequency below   produces zero kinetic energy; electrons are not emitted.

Significance of Einstein’s Equation

  1. Particle Nature of Light
    • Confirms light behaves as photons, not just waves.
  2. Explains Threshold Frequency
    • Electrons are emitted only if  .
  3. Energy Conservation
    • Total photon energy = work function + kinetic energy of electron.
  4. Foundation of Quantum Physics
    • Supports quantization of energy in light-matter interactions.
  5. Technological Applications
    • Basis for photoelectric cells, solar panels, photodetectors, and other optoelectronic devices.

Experimental Verification

  • Using a photoelectric setup, electrons are ejected from a metal surface under light illumination.
  • Varying the frequency of light confirms that:
    1. Electrons are not emitted below a threshold frequency.
    2. Kinetic energy increases with frequency.
    3. Number of electrons depends on intensity, but energy depends on frequency.
  • These results match Einstein’s equation exactly.
Conclusion

Einstein’s photoelectric equation,  , provides a quantitative explanation of the photoelectric effect. It shows that electrons are emitted only when the photon energy exceeds the metal’s work function, and the remaining energy appears as the kinetic energy of electrons. This equation confirmed the particle nature of light, explained the threshold frequency, and laid the foundation for quantum theory and modern optoelectronics, making it a cornerstone of 20th-century physics.