Planck’s law

What is Planck’s Law?

Planck’s law, also known as Planck’s radiation law, is a fundamental principle of physics that describes the radiation emitted by a blackbody at a given temperature. It was first formulated by the German physicist Max Planck in 1900, and it played a crucial role in the development of quantum mechanics. Planck’s law is considered one of the most important laws in physics and is widely used in various fields of science and engineering.

Blackbody Radiation

A blackbody is an idealized object that absorbs all radiation that falls on it and emits radiation at all wavelengths. Blackbodies are used as models for real objects in many fields of science, such as astrophysics, where stars can be approximated as blackbodies. The radiation emitted by a blackbody is called blackbody radiation, and it has a unique spectral distribution that depends only on the temperature of the object. Planck’s law describes this spectral distribution of blackbody radiation, and it has been experimentally verified to be accurate to a high degree of precision.

Formula and Example

Planck’s law gives the spectral radiance of blackbody radiation as a function of wavelength λ and temperature T. The formula is:

B(λ, T) = (2hc²/λ⁵) x 1/(ehc/λkT – 1)

where B(λ, T) is the spectral radiance, h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant, λ is the wavelength, and T is the temperature in Kelvin. This formula is used to calculate the intensity of radiation at each wavelength for a given temperature. For example, at a temperature of 5000 K, the spectral radiance of a blackbody peaks at a wavelength of about 580 nm, which corresponds to yellow-green light.

Application and Significance

Planck’s law has many applications in various fields of science and engineering. It is used in astronomy to analyze the spectra of stars and galaxies and to determine their temperatures and compositions. It is also used in materials science to study the thermal properties of materials and to design energy-efficient devices. Planck’s law played a crucial role in the development of quantum mechanics, as it showed that the energy of radiation is quantized, and it provided a theoretical basis for the concept of photons. Overall, Planck’s law is an essential tool for understanding the behavior of radiation and its interactions with matter.