Wien’s law, also known as Wien’s displacement law, describes the relationship between the temperature of an object and the peak wavelength of light it emits. It states that the product of the peak wavelength and the temperature of a black body is a constant value known as Wien's constant. As the temperature of an object increases, the peak wavelength of the emitted light shifts towards shorter wavelengths. It was derived in the year 1893 by a German Physicist Wilhelm Wien.

Wien’s Law & Black Body Radiation

According to Wien's displacement law, the value of the maximum wavelength of black-body radiation decreases as the absolute temperature of the object increases. 

When a black body is at a higher temperature, its constituent particles (atoms or molecules) possess higher average kinetic energies. In the context of radiation, these higher-energy particles emit photons with higher energies. 

The energy of a photon is directly proportional to its frequency, which is given by the equation:

where E is energy, h is Planck's constant, and ν is the frequency of the photon

Speed of light (c) is constant. Therefore, the relationship between the frequency (ν) and the wavelength (λ) of a photon is given by the equation: 

Combining the two equations above,

This equation shows that as the energy (E) of the emitted photon increases (due to higher temperature), the wavelength (λ) of the emitted light decreases.

As a result, at higher temperatures, more high-energy photons are emitted, and the peak of the black body radiation curve shifts towards shorter wavelengths. This is why, according to Wien's displacement law, the maximum wavelength of black-body radiation decreases as the absolute temperature of the object increases.

Wien's constant (b) is a physical constant that plays a crucial role in describing this relationship. It is the product of the temperature and the maximum wavelength of the black body radiation.

Mathematical representation of Wien’s law:

Where, λ_m - the maximum wavelength corresponding to the maximum intensity

T - The absolute temperature in Kelvins

b - Wien’s Constant = 2.88 x 10^-3 m-K or 0.288 cm-K

Applications of Wien’s Law

Wien's law has several important applications across various fields. Notable applications include:

• Astrophysics: Wien's law is used to determine the temperature of stars and analyze their spectra, aiding in stellar classification and understanding stellar evolution.
  • Temperature of the Sun: It can be used to calculate the temperature of the Sun by examining its peak emission wavelength. For example, if the peak wavelength falls in the green spectrum (around 500 nm), which is within the human eye's sensitive range, it indicates the Sun's temperature range.
• Thermal Imaging: In thermal imaging technology to estimate temperatures based on the peak wavelength of emitted infrared radiation, enabling applications in the fields including industrial inspections and medical thermography.
• Lighting Technology: It is crucial for designing and optimizing lighting systems, allowing the selection of light sources with specific color temperatures to achieve desired lighting effects.
  • Incandescent Bulb Light: Incandescent light bulbs work by heating a filament to high temperatures, causing it to emit light. As the temperature of the filament decreases, according to Wien's law, the peak wavelength of the emitted light shifts towards longer wavelengths. This means that as the filament cools down, the light emitted by the bulb appears redder. The phenomenon can be observed when turning off an incandescent bulb and noticing a reddish glow as it cools.
• Materials Science: This law is applied in the study of thermal properties of materials, aiding in the understanding of heat transfer, energy conversion, and material characterization.