Tru Physics

Ultraviolet Catastrophe

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Introduction

The Ultraviolet Catastrophe refers to a historical paradox in the theory of radiation of heated objects. This paradox resulted from the contradiction between the classical physics laws and experimental observations related to black body radiation at the end of the 19th century.

Classical Predictions and the Problem

According to the classical theory of electromagnetic radiation, the energy of a resonator (an oscillating system capable of absorbing or emitting radiation) is proportional to the frequency of its oscillation. This led to the Rayleigh-Jeans law, which predicted the energy density of black-body radiation as follows:

u(\nu, T) = \dfrac{8\pi\nu^2k_BT}{c^3}

where u(\nu, T) is the energy density, \nu is the frequency, T is the absolute temperature, k_B is the Boltzmann constant, and c is the speed of light.

However, this law predicts that the energy radiated by a black body at high frequencies (short wavelengths, in the ultraviolet region and beyond) should become infinitely large, which is not observed in reality. This contradiction was known as the Ultraviolet Catastrophe.

Resolution by Planck

The Ultraviolet Catastrophe was resolved by Max Planck in 1900. Planck modified the Rayleigh-Jeans law by assuming that the energy of the oscillators is quantized, meaning it can only take on discrete values. The energy of each oscillator was given by E = nh\nu, where h is Planck’s constant, \nu is the frequency of the oscillator, and n is an integer. This led to the formulation of the Planck’s law:

u(\nu, T) = \dfrac{8\pi h\nu^3}{c^3}\dfrac{1}{e^{\frac{h\nu}{k_BT}} - 1}

Planck’s law accurately predicted the energy distribution of black-body radiation at all frequencies, resolving the Ultraviolet Catastrophe.

Impact on Physics

The resolution of the Ultraviolet Catastrophe marked the birth of quantum mechanics. Planck’s assumption of energy quantization was a revolutionary idea that led to the development of quantum theory, fundamentally changing our understanding of the physical world. This theory has since become one of the most successful theories in the history of physics, explaining a vast array of physical phenomena from the microscopic to the macroscopic level.

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