Black-body radiation
The electromagnetic radiation emitted by an idealized perfect absorber and emitter of radiation at a given temperature, following Planck's law.
Black-body radiation
Black-body radiation represents a fundamental concept in quantum mechanics and thermal physics, describing the electromagnetic radiation emitted by a theoretical perfect absorber and emitter of radiation, known as a black body. This phenomenon played a crucial role in the development of modern physics, particularly through Max Planck's groundbreaking work in 1900.
Physical Characteristics
A black body exhibits several key properties:
- Absorbs 100% of incident electromagnetic radiation
- Emits radiation across all wavelengths
- Emission spectrum depends solely on temperature
- Follows Stefan-Boltzmann law for total radiation intensity
Historical Significance
The study of black-body radiation led to what became known as the ultraviolet catastrophe, where classical physics incorrectly predicted infinite energy at short wavelengths. This discrepancy prompted Planck to introduce the revolutionary concept of energy quantization, marking the birth of quantum theory.
Mathematical Description
The spectral radiance of a black body is described by Planck's law:
B(λ,T) = (2hc²/λ⁵) * 1/(e^(hc/λkT) - 1)
Where:
- h is Planck's constant
- c is the speed of light
- λ is wavelength
- T is absolute temperature
- k is Boltzmann constant
Applications
Black-body radiation finds practical applications in:
- Astronomical observations for determining stellar temperatures
- Industrial temperature measurement
- Cavity radiators for calibration standards
- Understanding cosmic microwave background radiation
Related Phenomena
Several natural and artificial phenomena approximate black-body behavior:
- Solar radiation
- Incandescent light emission
- Thermal imaging systems
- Wien's displacement law describing peak wavelength
Modern Implications
Understanding black-body radiation remains crucial for:
- Climate science and atmospheric modeling
- Materials science and heat transfer
- Quantum optics
- Radiation thermometry
The concept continues to influence modern physics and technology, providing a foundation for understanding thermal radiation and quantum behavior of light and matter.