The inability of classical electromagnetic wave theory to fully explain black body radiation was a significant problem in the late 19th century, known as the "ultraviolet catastrophe." Classical wave theory predicted that as the frequency of electromagnetic waves approached higher and higher values, the energy would also increase without bound. This prediction was inconsistent with experimental observations of black body radiation, which showed that the intensity of radiation peaked at a certain frequency and then decreased at higher frequencies.
The resolution to this problem came with the development of quantum mechanics and Max Planck's introduction of the concept of energy quantization. Planck proposed that the energy of electromagnetic radiation is quantized and can only exist in discrete packets or "quanta," where the energy of each quantum is proportional to the frequency of the radiation.
Planck's theory, known as Planck's radiation law, provided a mathematical expression that successfully described the observed black body radiation spectrum. It introduced the idea that electromagnetic radiation is quantized and can be thought of as composed of discrete energy packets called photons.
In contrast to classical wave theory, quantum mechanics and the concept of quantized energy were able to explain the observed behavior of black body radiation accurately. This development marked a significant departure from classical physics and led to the development of quantum electrodynamics (QED), which successfully describes the behavior of electromagnetic radiation and its interactions with matter at both macroscopic and microscopic scales.
In summary, classical electromagnetic wave theory was unable to explain black body radiation because it did not incorporate the concept of quantized energy. Quantum mechanics, with its understanding of energy quantization and the photon nature of electromagnetic radiation, provided a successful explanation for black body radiation and led to the development of modern quantum electrodynamics.