Wien’s Displacement Law Explained

Wien’s Displacement Law is a scientific principle that describes the relationship between temperature and the wavelength of the maximum intensity of radiation emitted by a black body. Simply put, this law states that as the temperature of an object increases, the wavelength of the radiation it emits decreases. This principle is essential in understanding the behavior of electromagnetic radiation and is used in many fields of physics, including astronomy, astrophysics, and cosmology.

The law is named after Austrian physicist Wilhelm Wien, who first proposed it in 1893. Wien’s work on the law earned him the Nobel Prize in Physics in 1911. The discovery of this law was crucial in the development of our current understanding of the electromagnetic spectrum, as it provided a quantitative explanation for the spectral distribution of black body radiation.

The Formula for Wien’s Displacement Law

The mathematical formula for Wien’s Displacement Law is given by:

λ_max = b/T

where λ_max is the wavelength of the maximum intensity of radiation emitted by the black body, T is the temperature of the black body in Kelvin, and b is a constant called Wien’s displacement constant, equal to 2.898 × 10^-3 m·K.

This formula shows that the wavelength of maximum radiation intensity decreases as the temperature of the black body increases. It also shows that the wavelength is inversely proportional to the temperature, meaning that as one increases, the other decreases.

Applications of Wien’s Displacement Law

Wien’s Displacement Law has numerous applications in various fields of physics. For instance, it is used in astronomy to determine the temperature of stars based on the wavelength of the maximum intensity of radiation they emit. The law is also used in the design of incandescent bulbs, where it is essential to know the temperature of the filament to produce the desired wavelength of light.

Furthermore, the law is used in the study of the cosmic microwave background radiation, which is believed to be the remnants of the Big Bang. Wien’s Displacement Law provides a way to estimate the temperature of the universe based on the wavelength of this radiation.

Overall, Wien’s Displacement Law is an important principle in physics that has numerous practical applications in various fields of study.

Example Calculation of Wien’s Displacement Law

Suppose we have a black body with a temperature of 1000 K. Using Wien’s Displacement Law, we can calculate the wavelength of the maximum intensity of radiation emitted by the black body:

λ_max = b/T = 2.898 × 10^-3 m·K / 1000 K = 2.898 × 10^-6 m

Therefore, the maximum intensity of radiation emitted by the black body occurs at a wavelength of 2.898 × 10^-6 m (or 2898 nm), which falls in the infrared region of the electromagnetic spectrum. This calculation demonstrates how Wien’s Displacement Law can be used to predict the behavior of black body radiation based on the temperature of the object.