The difference between quantum theory and electromagnetic wave theory lies in their fundamental descriptions of radiation and how they explain the intensity of radiation.
Electromagnetic wave theory, also known as classical electrodynamics, treats electromagnetic radiation as continuous waves. According to this theory, the intensity of radiation is directly related to the amplitude of the wave. In other words, the more energy carried by the wave, the higher the intensity of radiation. This relationship is described by the Poynting vector, which represents the direction and magnitude of the energy flow in an electromagnetic wave.
On the other hand, quantum theory, specifically quantum electrodynamics (QED), describes radiation as consisting of discrete packets of energy called photons. According to quantum theory, the intensity of radiation is related to the number of photons present rather than the amplitude of a continuous wave. The intensity is determined by the rate at which photons are emitted or absorbed by a source.
In quantum theory, the energy of each individual photon is directly proportional to its frequency (E = hf), where h is Planck's constant and f is the frequency of the radiation. This means that higher-frequency photons (such as X-rays or gamma rays) carry more energy per photon compared to lower-frequency photons (such as radio waves or visible light).
To determine the total intensity of radiation, quantum theory considers the number of photons per unit time passing through a given area. The intensity is measured in terms of the number of photons or the energy carried by those photons.
In summary, the electromagnetic wave theory of radiation relates the intensity to the amplitude of a continuous wave, while quantum theory associates the intensity with the number of photons and their energy.