Planck's law

Planck's Law

Planck's law, also known as Planck's radiation law, is a fundamental principle in physics that describes the spectral energy density of electromagnetic radiation emitted by a black body at a given temperature. It was formulated by the German physicist Max Planck in 1900 and played a crucial role in the development of quantum mechanics.

Background

Before the formulation of Planck's law, classical physics failed to explain certain phenomena related to the emission and absorption of electromagnetic radiation. According to classical theory, a black body should emit an infinite amount of energy at all wavelengths, which contradicted experimental observations. Planck's law provided a breakthrough by introducing the concept of quantization of energy.

Formulation

Planck's law states that the spectral energy density of radiation emitted by a black body at a given temperature is proportional to the frequency of the radiation and inversely proportional to the wavelength. Mathematically, it can be expressed as:

E(λ, T) = (2hc²/λ³) * (1/(e^(hc/λkT) - 1))

where: - E(λ, T) is the spectral energy density at wavelength λ and temperature T, - h is Planck's constant, - c is the speed of light, - k is the Boltzmann constant, and - e is the base of the natural logarithm.

Significance

Planck's law revolutionized our understanding of the behavior of electromagnetic radiation. It provided a theoretical explanation for the observed distribution of energy emitted by black bodies at different temperatures, known as the black body radiation spectrum. This spectrum follows a characteristic shape, with a peak intensity that shifts towards shorter wavelengths as the temperature increases.

Applications

Planck's law has numerous applications in various fields of science and technology. Some notable applications include:

1. Astrophysics: Planck's law is used to study the radiation emitted by stars and other celestial objects. By analyzing the spectral energy density, astronomers can determine the temperature and composition of these objects.

2. Thermodynamics: Planck's law is fundamental to the study of thermal radiation and plays a crucial role in understanding heat transfer and energy conversion processes.

3. Quantum mechanics: Planck's law was a key inspiration for the development of quantum mechanics. It introduced the concept of energy quantization, which laid the foundation for the wave-particle duality of light and matter.

See Also

- Black body radiation - Max Planck - Quantum mechanics

References

1. Planck, M. (1901). "Über das Gesetz der Energieverteilung im Normalspectrum." Annalen der Physik, 309(3), 553-563.

2. Kittel, C., & Kroemer, H. (1980). "Thermal Physics." W. H. Freeman and Company.

3. Griffiths, D. J. (2005). "Introduction to Quantum Mechanics." Pearson Education.