We will review the wave properties of light (wavelength and spectrum) and its particle properties (photons and the photoelectric effect), and organize the overall picture of electromagnetic waves.
Basic Knowledge
Wavelength range of visible light: Approximately 380 nm (violet) to 780 nm (red).
Electromagnetic spectrum (from longer to shorter wavelengths):
Radio waves → microwaves → infrared rays → visible light → ultraviolet rays → X-rays → γ-rays
All propagate through a vacuum at speed c = 3.0×10⁸ m/s.
Photon (photon): Light also behaves as a packet of energy (a quantum).
Energy of one photon: E = hf = hc/λ (h = 6.63×10⁻³⁴ J·s: Planck constant)
Photoelectric effect (photoelectric effect): The phenomenon in which electrons are emitted when light is shone on a metal. It occurs when the frequency is at least a certain value (threshold frequency f₀).
hf = W + (1/2)mv²max (W = hf₀: work function, (1/2)mv²max: maximum kinetic energy of photoelectrons)
Photon (light quantum, photon) (The smallest unit of light energy. E = hf)
Planck constant h = 6.63×10⁻³⁴ J·s
Photoelectric effect (photoelectric effect) (The phenomenon in which light strikes a metal and electrons are emitted. Frequency-dependent)
Work function W [J or eV] (The minimum energy required to remove an electron from a metal)
Threshold frequency f₀ (The minimum frequency at which the photoelectric effect occurs. f₀ = W/h)
Further Study (Background and Significance)
Einstein explained the photoelectric effect using the photon hypothesis in 1905 and received the 1921 Nobel Prize in Physics for it (not for the theory of relativity). Its “frequency dependence,” which could not be explained by classical electromagnetic wave theory, became a starting point for quantum theory.
The dual nature of light (wave nature + particle nature) is central to modern physics. Interference, diffraction, and polarization are evidence of its wave nature, while the photoelectric effect and Compton scattering are evidence of its particle nature. de Broglie extended this idea to matter waves (electrons also have a wavelength λ = h/p).
The spectrum of sunlight can be approximated as blackbody radiation, and the temperature of the Sun’s surface (approximately 5800 K) can be estimated from the wavelength of its peak (Wien’s displacement law).
- Visible light: 380 nm (violet) to 780 nm (red)
- Electromagnetic waves: radio waves→microwaves→infrared→visible→ultraviolet→X-rays→γ-rays
- Photon energy E = hf = hc/λ
- Photoelectric effect condition: hf ≥ W (frequency at least the threshold value)
- Maximum kinetic energy: (1/2)mv²max = hf − W
Points to Note (Easily Confused)
① The photoelectric effect depends not on light intensity but on frequency (classical wave theory predicts intensity dependence, which contradicts experiments). ② The f in E = hf is the frequency of light (independent of the medium). λ changes in a medium, but f does not. ③ The units of the work function W may be eV or J. 1 eV = 1.6×10⁻¹⁹ J. ④ Threshold wavelength λ₀ = hc/W (longer wavelength = lower frequency = insufficient energy → the photoelectric effect does not occur).
Practice
- Find the energy of one photon of light with frequency 6.0×10¹⁴ Hz (h = 6.6×10⁻³⁴ J·s).
- Light of frequency f is shone on a metal with work function W = 2.0 eV, and photoelectrons with maximum kinetic energy 1.0 eV are emitted. Find hf in eV.
- From the viewpoint of photons, explain why the photoelectric effect is determined not by “light intensity” but by “light frequency.”