Rayleigh-Jeans Law

Definition

The Rayleigh-Jeans Law describes the spectral radiance of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature, predicting that the radiance increases with frequency and diverges at high frequencies. This law successfully explains the behavior of black-body radiation at long wavelengths but fails at short wavelengths, leading to the ultraviolet catastrophe, which paved the way for the development of quantum mechanics and Planck's distribution.

5 Must Know Facts For Your Next Test

1. The Rayleigh-Jeans Law is mathematically expressed as $$ B( u, T) = \frac{8\pi\nu^2}{c^3}kT $$, where $$ B $$ is the spectral radiance, $$ \nu $$ is the frequency, $$ k $$ is the Boltzmann constant, and $$ T $$ is the absolute temperature.
2. At low frequencies (or long wavelengths), the Rayleigh-Jeans Law accurately predicts the spectral radiance of black-body radiation.
3. As frequency increases, the predicted radiance approaches infinity according to the Rayleigh-Jeans Law, leading to discrepancies with experimental data at ultraviolet frequencies.
4. The failure of the Rayleigh-Jeans Law at high frequencies prompted Max Planck to propose a new model that incorporated quantized energy levels, leading to Planck's Law.
5. This law fundamentally changed our understanding of thermal radiation and marked a significant turning point towards modern quantum theory.

Review Questions

• How does the Rayleigh-Jeans Law explain black-body radiation at low frequencies, and what is its limitation at high frequencies?
  • The Rayleigh-Jeans Law successfully describes black-body radiation at low frequencies by showing that spectral radiance increases with frequency. However, its limitation arises at high frequencies where it predicts an infinite increase in radiance, resulting in a phenomenon known as the ultraviolet catastrophe. This inconsistency with experimental results highlighted the inadequacy of classical physics to fully explain black-body radiation.
• In what ways did the shortcomings of the Rayleigh-Jeans Law contribute to the development of quantum mechanics?
  • The shortcomings of the Rayleigh-Jeans Law, particularly its failure to account for the observed behavior of black-body radiation at short wavelengths, played a critical role in advancing quantum mechanics. The discrepancy between classical predictions and experimental findings led Max Planck to propose that energy is quantized. This revolutionary idea laid the groundwork for quantum theory, shifting our understanding of physical phenomena and paving the way for subsequent developments in modern physics.
• Evaluate the significance of the Rayleigh-Jeans Law in historical context, particularly concerning its role in transitioning from classical physics to quantum mechanics.
  • The significance of the Rayleigh-Jeans Law lies in its role as a bridge between classical physics and quantum mechanics. While it accurately described black-body radiation at low frequencies, its failure at high frequencies illustrated key limitations in classical theories. This discrepancy catalyzed a reevaluation of existing scientific frameworks, leading to Max Planck's introduction of quantization. The subsequent acceptance of Planck's Law and quantum principles transformed our understanding of energy and matter, marking a foundational shift in modern physics that continues to influence scientific inquiry today.

Related terms

Black-body Radiation: The idealized physical concept of an object that absorbs all incident electromagnetic radiation, regardless of frequency or angle, and emits radiation in a characteristic spectrum determined solely by its temperature.

Planck's Law:

A law that describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium, taking into account quantization of energy, resolving the limitations of the Rayleigh-Jeans Law.

Ultraviolet Catastrophe: The phenomenon where classical physics predicted infinite energy emission at ultraviolet wavelengths for black-body radiation, leading to a contradiction with experimental results and highlighting the need for quantum theory.