Planck’s Law of Black Body Radiation, formulated by the German physicist Max Planck in 1900, is a fundamental principle in the field of quantum mechanics and thermal physics. This law describes the spectral distribution of electromagnetic radiation emitted by a perfect black body at a given temperature. A black body is an idealized object that absorbs all incident radiation and emits radiation over a wide range of frequencies and wavelengths.
Key features and principles of Planck’s Law of Black Body Radiation include:
- Quantization of Energy: Planck’s groundbreaking insight was that energy is not continuous but quantized, meaning it can only exist in discrete, indivisible units called “quanta.” This concept was a precursor to the development of quantum mechanics.
- Spectral Distribution: The law describes the distribution of radiation intensity across different wavelengths (or frequencies) of electromagnetic radiation. It predicts how much energy is emitted at each wavelength for a black body at a given temperature.
- Temperature Dependence: Planck’s Law shows that the spectral distribution of black body radiation is highly temperature-dependent. As the temperature of the black body increases, the intensity of radiation at all wavelengths also increases.
- Ultraviolet Catastrophe Resolution: Prior to Planck’s work, a theoretical problem known as the “ultraviolet catastrophe” existed in physics. Classical physics predicted that black body radiation would diverge to infinity at short wavelengths, which was not observed experimentally. Planck’s quantization of energy resolved this problem by introducing a minimum energy quantum (hν) associated with each frequency ν.
The mathematical form of Planck’s Law can be expressed as:
[B(\lambda, T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{\frac{hc}{\lambda kT}} – 1}]
Where:
- (B(\lambda, T)) is the spectral radiance (intensity) at a specific wavelength λ for a black body at temperature T.
- (h) is Planck’s constant.
- (c) is the speed of light in a vacuum.
- (k) is the Boltzmann constant.
Planck’s Law accurately describes the spectral distribution of radiation emitted by black bodies across a wide range of temperatures and wavelengths. It played a pivotal role in the development of quantum theory and had a profound impact on our understanding of the behavior of matter and energy at the atomic and subatomic levels. Additionally, it laid the foundation for the later development of quantum mechanics by demonstrating the quantization of energy, a fundamental concept in modern physics.