MP Board · Class 12 · Physics · Dual Nature of Radiation and MatterExplain Einstein's photoelectric equation and discuss how it successfully explains the experimental observations of the photoelectric effect. State the laws of photoelectric emission.

Introduction to Einstein's Photoelectric Equation\nAlbert Einstein successfully explained the photoelectric effect in 1905 using Max Planck's quantum theory of radiation. According to Einstein, light radiation travels in discrete packets of energy called photons. The energy of each photon is given by $E = h\nu$, where $h$ is Planck's constant and $\nu$ is the frequency of the incident radiation.

Mechanism of Photoelectric Emission\nWhen a photon of sufficient energy is incident on a metal surface, it collides with an electron inside the metal and transfers its entire energy to the electron in a single, instantaneous interaction. A part of this energy is used to liberate the electron from the attractive forces of the metal surface, which is called the work function ($\phi_0$ or $h\nu_0$). The remaining energy appears as the maximum kinetic energy ($K_{max}$) of the emitted photoelectrons.

Mathematical Formulation\nAccording to the conservation of energy, the energy of the incident photon is expressed as:

$$h\nu = \phi_0 + K_{max}$$\nAlternatively, in terms of stopping potential ($V_0$): $$h\nu = h\nu_0 + eV_0$$\nwhere $e$ is the charge of an electron, $\nu_0$ is the threshold frequency, and $K_{max} = eV_0$.

Explanation of Experimental Observations

1. Effect of Frequency: As the frequency of incident light increases, the maximum kinetic energy of emitted photoelectrons increases linearly, provided the frequency is greater than the threshold frequency. Below the threshold frequency, emission is impossible.
2. Intensity Independence of Kinetic Energy: Increasing the intensity of incident light increases the number of photons striking the surface per second, thereby increasing the photoelectric current (number of electrons emitted), but it has no effect on the maximum kinetic energy of the emitted photoelectrons.
3. Instantaneous Emission: The collision between a photon and an electron is instantaneous. There is no time lag between the incidence of light and the emission of photoelectrons.

Laws of Photoelectric Emission

• For a given photosensitive material, there is a minimum frequency called the threshold frequency below which no photoelectrons are emitted, regardless of how intense the incident light is.
• The photoelectric current is directly proportional to the intensity of the incident radiation, provided the frequency is above the threshold value.
• The maximum kinetic energy of the emitted photoelectrons is independent of the intensity of the incident radiation and depends only on the frequency of the incident light.
• The photoelectric emission is an instantaneous process.