The Feynman Lecture | volume 3 | chapter 4 | Black body radiation law and exclusion principle

The black body radiation law, or Planck's law, describes the distribution of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. A black body is an idealized object that perfectly absorbs and emits all radiation at every wavelength.

Planck's law, derived by Max Planck in 1900, is given by:

B(\lambda, T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{\frac{hc}{\lambda k T}} - 1}

where:

is the spectral radiance (power per unit area per unit wavelength) at wavelength and temperature ,

is Planck's constant,

is the speed of light,

is Boltzmann's constant,

is the wavelength, and

is the absolute temperature of the black body.


Key concepts related to black body radiation include:

1. Wien's Displacement Law: This law states that the wavelength at which the radiation is most intense is inversely proportional to the temperature. Mathematically, , where .


2. Stefan-Boltzmann Law: This law states that the total energy emitted across all wavelengths per unit area is proportional to the fourth power of the temperature. , where is the Stefan-Boltzmann constant.



These laws are fundamental in fields like astrophysics, quantum mechanics, and thermodynamics, as they help to understand the thermal radiation of objects, including stars and planets.

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