Fix the mistake: Atoms and Nuclei

The Photoelectric Effect and the Particle Nature of Light

Einstein explained the photoelectric effect using the particle nature of light (photons), opening the door to quantum theory.

Basic Knowledge

Photoelectric effect: The phenomenon in which electrons (photoelectrons) are emitted when light strikes a metal surface.
Experimental facts that classical electromagnetism cannot explain:
① Below the threshold frequency f₀, corresponding to the work function W, no electrons are emitted even if the light is intense
② The maximum kinetic energy of electrons is independent of light intensity and is determined only by frequency
③ Even weak light immediately ejects electrons if its frequency is high enough

Einstein’s light-quantum hypothesis:
Light consists of particles（photons）with energy E = hf.

Maximum kinetic energy of photoelectrons:
K_max = hf − W（W: work function = minimum energy required to remove an electron from the metal）
Threshold frequency: f₀ = W/h（hf₀ = W）

Important Terms
Photoelectric effect (photoelectric effect)（the phenomenon in which electrons are emitted from a metal when light shines on it）
Photon (photon)（a particle of light with energy E = hf）
Work function W (work function)（the minimum energy required to remove an electron from a metal）
Threshold frequency f₀（the minimum frequency at which the photoelectric effect occurs. hf₀ = W）
Wave-particle duality of light（light has both wave and particle properties）

Further Exploration (Background and Significance)

Einstein published this paper in 1905 (his “miracle year”) and received the 1921 Nobel Prize in Physics（the prize was awarded for his research on the photoelectric effect, not the theory of relativity）.
Wave-particle duality: Young’s interference experiment demonstrates wave behavior, while Compton scattering and the photoelectric effect demonstrate particle behavior. Which “face” appears depends on the experimental setup（wave-particle duality）.
The photoelectric effect is the basic principle of solar power generation: when light strikes a semiconductor, electrons are excited and current flows（the photovoltaic effect）. However, because it occurs inside a semiconductor, it is not exactly the same as the photoelectric effect on a metal surface.

Key Points
  • E = hf（photon energy）
  • K_max = hf − W（maximum kinetic energy of photoelectrons）
  • Threshold frequency f₀ = W/h
  • Electron emission is determined by frequency, not intensity
  • Photoelectric effect → evidence of the particle nature of light
  • Wave-particle duality: interference→wave nature, photoelectric effect→particle nature
  • Einstein’s 1921 Nobel Prize

Notes (Easily Confused Points)

① Even if the light is intensified, no electrons are emitted when f < f₀. Distinguish intensity from frequency. ② K_max is linearly proportional to frequency (hf − W). ③ W differs depending on the type of metal. ④ Increasing light intensity increases the number of photons（K_max remains unchanged）and increases the current.

Practice

  1. When light with frequency f = 1.2 × 10¹⁵ Hz shines on a metal with work function W = 4.8 × 10⁻¹⁹ J, find the maximum kinetic energy of the photoelectrons（h = 6.6 × 10⁻³⁴ J·s）.
  2. Find the threshold frequency of this metal.
  3. What happens to the maximum kinetic energy of the photoelectrons when the light intensity is doubled?

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