Question

The ultraviolet catastrophe in the classical (Rayleigh-Jeans) theory of cavity radiation is attributed to the assumption that

• A. the standing waves of all allowed frequencies in the cavity have the same average energy
• B. the density of the standing waves in the cavity is independent of the shape and size of the cavity
• C. the allowed frequencies of the standing waves inside the cavity have no upper limit
• D. the number of allowed frequencies for the standing waves in a frequency range v to (v + dv) is proportional to v²

Answer 1

The Correct Option is A

The Rayleigh-Jeans theory of cavity radiation assumes that the standing waves of all allowed frequencies in the cavity have the same average energy. This assumption leads to an overestimation of the energy at high frequencies, a phenomenon known as the ultraviolet catastrophe.

Explanation:

The assumption in option (A) implies that every frequency mode contributes equally to the radiation energy. At high frequencies, this leads to the prediction of infinite energy, resulting in the ultraviolet catastrophe.

This assumption was later corrected by Planck’s quantization of energy in the Planck radiation law, which introduced the concept that energy is emitted or absorbed in discrete packets called quanta.

Conclusion:

Thus, the Rayleigh-Jeans assumption in option (A) directly leads to the ultraviolet catastrophe.