What describes the relationship between wavelength and energy in a wave?

The relationship between wavelength and energy in a wave is that shorter wavelengths correspond to higher energy. This is particularly evident in the context of electromagnetic waves, such as light. The energy of a photon (a particle of light) is inversely proportional to its wavelength; as the wavelength decreases, the energy increases. The formula that illustrates this relationship is E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

In this equation, it's clear that for a given speed of light and constant Planck's constant, a decrease in wavelength (indicating that the wave is more compressed) results in an increase in energy. Therefore, shorter wavelengths carry more energy compared to longer wavelengths, making the understanding of this concept essential in various fields, such as physics and chemistry, particularly when discussing phenomena like electromagnetic radiation and quantum mechanics.