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What is the photoelectric effect?

Class 12 PhysicsNCERT chapter: Dual Nature of Radiation and Matterइसे हिंदी में पढ़ें

Exam-ready answer

The photoelectric effect is the emission of electrons from a metal surface when light of suitable frequency falls on it. Emission occurs only if the frequency is above a threshold frequency ν₀, whatever the intensity. Einstein explained it using photons: Kmax = hν − φ₀, where φ₀ = hν₀ is the work function of the metal.

Explanation

When ultraviolet light falls on a clean zinc plate, electrons called photoelectrons are emitted. Alkali metals such as sodium, potassium and caesium emit electrons even with visible light. In an evacuated tube, the emitted electrons travel from the emitter plate to a collector plate and form a photoelectric current. The negative collector potential that just stops the most energetic electrons is the stopping potential V₀, with eV₀ = Kmax.

Experiments show four facts. Photocurrent is proportional to the intensity of light. The stopping potential, and hence the maximum kinetic energy, depends on frequency but not on intensity. Below the threshold frequency ν₀ no electrons are emitted, however intense the light. Emission is practically instantaneous, even with very dim light. The wave theory of light cannot explain the last three facts.

Einstein proposed that light consists of photons, each with energy E = hν, where h = 6.63 × 10⁻³⁴ J s is Planck's constant. One photon gives all its energy to one electron. Part of it, the work function φ₀, frees the electron from the metal; the rest becomes kinetic energy: Kmax = hν − φ₀, or eV₀ = hν − φ₀. If hν < φ₀, no electron escapes. Brighter light means more photons, so more electrons, but not faster ones.

Points to remember

  1. Photoelectric effect: emission of electrons from a metal surface by light of suitable frequency.
  2. Einstein's photoelectric equation: Kmax = hν − φ₀ = eV₀.
  3. Work function φ₀ = hν₀: the minimum energy needed to remove an electron from the metal, usually expressed in electron volts (eV).
  4. Photocurrent is proportional to intensity; Kmax and V₀ depend on frequency, not on intensity.
  5. No emission below the threshold frequency ν₀; emission is instantaneous.

Exam tip

Write Einstein's equation Kmax = hν − φ₀ and the relation eV₀ = Kmax. Sketch the graph of stopping potential against frequency: a straight line with slope h/e that cuts the frequency axis at ν₀.

Questions students also ask

What is threshold frequency?
Threshold frequency ν₀ is the minimum frequency of incident light that can eject electrons from a given metal. It is related to the work function by φ₀ = hν₀. Light below this frequency cannot cause emission, however bright it is, because each photon has too little energy.
Why can't the wave theory explain the photoelectric effect?
In wave theory, energy is spread over the wavefront and absorbed gradually. So brighter light should give faster electrons, any frequency should work if the light is intense enough, and dim light should cause a time lag. Experiments show none of these, while the photon picture explains all of them.
What is stopping potential?
Stopping potential V₀ is the minimum negative potential given to the collector plate that just stops the most energetic photoelectrons, making the photocurrent zero. It measures the maximum kinetic energy, eV₀ = Kmax, and increases linearly with the frequency of the incident light.

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