Short Answer

The ultraviolet catastrophe refers to the failure of classical physics to correctly predict the radiation emitted by a blackbody at high frequencies. According to classical theory, the intensity of radiation should increase without limit in the ultraviolet region. This meant the blackbody should emit infinite energy at short wavelengths, which was impossible.

Experiments showed that the actual intensity decreases at high frequencies. This mismatch between classical prediction and observed results is called the ultraviolet catastrophe. Max Planck solved this problem by introducing the idea that energy is emitted in small packets called quanta, leading to the birth of quantum theory.

Detailed Explanation :

Ultraviolet catastrophe

The ultraviolet catastrophe was one of the biggest failures of classical physics in the late 19th century. It refers to the incorrect prediction made by classical theories about the distribution of energy in blackbody radiation. A blackbody is an ideal object that absorbs all radiation and emits energy depending only on its temperature. Scientists measured how much energy a blackbody emits at different wavelengths and found a smooth curve: low intensity at long wavelengths, rising to a peak, and then falling at short wavelengths.

Classical physics attempted to explain this using the Rayleigh-Jeans law, which was based on electromagnetic theory and the equipartition of energy. These classical ideas worked well at long wavelengths but failed at short wavelengths. According to the Rayleigh-Jeans law, the intensity of emitted radiation should continue increasing endlessly as wavelength becomes shorter. This suggested that at ultraviolet and even shorter wavelengths, the energy should become extremely large, even infinite.

This prediction was physically impossible. No real object emits infinite energy. Experimental data showed that at high frequencies, the intensity actually decreases instead of increasing. This clear contradiction between theory and experiment was named the ultraviolet catastrophe. It showed that classical physics could not describe radiation behaviour at microscopic levels and needed new ideas.

Classical explanation and its failure (Subheading)

Classical physics used the equipartition theorem to explain radiation inside a blackbody cavity. It stated that energy is shared equally among all possible modes of vibration. A cavity has an extremely large number of high-frequency vibration modes. If each of these modes has the same amount of energy, the total energy becomes extremely high, especially in the ultraviolet region.

The Rayleigh-Jeans law, based on this idea, predicted that intensity increases continuously with frequency. The mathematical equation showed that as wavelength approaches zero, the intensity approaches infinity. This prediction was the core of the ultraviolet catastrophe.

But experiments revealed the opposite behaviour. They showed that intensity rises only up to a certain point and then falls at shorter wavelengths. Classical laws could not explain why radiation peaks at a specific wavelength or why the peak shifts with temperature. They also failed to describe why energy distribution at high frequencies drops sharply. These mismatches proved that classical physics was incomplete.

Another failure was the belief that energy is continuous. Classical physics assumed that atoms could emit or absorb any amount of energy. But the behaviour of blackbody radiation suggested that energy does not behave continuously at microscopic levels.

Because of these reasons, classical physics broke down at explaining high-frequency radiation, and this breakdown was called the ultraviolet catastrophe.

Planck’s solution and the rise of quantum theory (Subheading)

The failure of classical physics led scientists to search for a new explanation. Max Planck provided the breakthrough in 1900. He proposed that energy is not continuous but is emitted or absorbed in small fixed units called quanta. The energy of each quantum is directly proportional to the frequency of radiation. Planck expressed this idea through the formula E = hν, where h is Planck’s constant.

Planck found that if energy is quantised, the predicted intensity curve matches the experimental results perfectly. This new idea explained why intensity increases at low frequencies and decreases at high frequencies. At short wavelengths, the energy of each quantum is large, so fewer quanta are emitted, which explains the drop in intensity. This solved the ultraviolet catastrophe.

Planck’s idea marked the beginning of quantum theory. It introduced a new way of thinking about energy, light, and matter. This theory later helped explain many other phenomena such as the photoelectric effect, atomic structure, and the stability of atoms. Quantum theory replaced classical ideas at microscopic levels and became the foundation of modern physics.

The ultraviolet catastrophe was therefore a turning point in science. It showed the limits of classical theories and opened the path for revolutionary changes in physics. Without this major failure, the development of quantum mechanics might not have happened so early.

Conclusion

The ultraviolet catastrophe refers to the incorrect prediction of infinite energy emission at short wavelengths by classical physics. Experiments proved this prediction wrong, showing that radiation intensity decreases at high frequencies. Classical physics failed because it assumed continuous energy distribution. Max Planck solved this problem by introducing quantised energy, leading to the birth of quantum theory. The ultraviolet catastrophe marks the shift from classical to modern physics and remains a key milestone in scientific history.