The relationship between energy and frequency in electromagnetic waves is described by Planck's equation and the photon model of light. According to Planck's equation:
E = h * f
where: E is the energy of a photon, h is Planck's constant (approximately 6.626 x 10^-34 joule-seconds), f is the frequency of the electromagnetic wave.
This equation suggests that the energy of a photon is directly proportional to its frequency. In other words, higher-frequency waves carry more energy per photon compared to lower-frequency waves.
This relationship is further supported by the wave-particle duality of light. Electromagnetic waves can exhibit both wave-like and particle-like properties. Each particle-like unit of light is called a photon, and its energy is quantized, meaning it can only exist in specific discrete amounts determined by its frequency.
For example, in the visible light spectrum, photons of higher-frequency violet light carry more energy than photons of lower-frequency red light. Similarly, in the broader electromagnetic spectrum, higher-frequency waves like X-rays and gamma rays have higher energy per photon compared to lower-frequency waves such as radio waves.
It's important to note that the relationship between energy and frequency holds for individual photons and not for the overall intensity or power of an electromagnetic wave, which depends on both the number of photons and their energy.