Shorter wavelengths have more energy than longer wavelengths because the energy of a wave is directly proportional to its frequency. This relationship is described by the equation:
E = h * f
where:
- E represents the energy of a wave
- h is Planck's constant (a fundamental constant in quantum mechanics)
- f is the frequency of the wave
According to this equation, the energy (E) of a wave is directly proportional to its frequency (f). Since wavelength (λ) and frequency are inversely related (i.e., higher frequency corresponds to shorter wavelength and vice versa), we can express this relationship as:
E = h * c / λ
where:
- c is the speed of light (a constant)
From this equation, we can see that as wavelength (λ) increases, the energy (E) decreases, and vice versa. Therefore, shorter wavelengths correspond to higher frequencies and higher energy levels.
This relationship can be observed in various forms of electromagnetic radiation. For example, in the electromagnetic spectrum, gamma rays have the shortest wavelengths, followed by X-rays, ultraviolet light, visible light, infrared radiation, microwaves, and radio waves, in increasing order of wavelength and decreasing order of energy. Gamma rays have the highest energy among these types of radiation, while radio waves have the lowest energy.
It's important to note that this relationship holds true for electromagnetic waves, but for other types of waves (such as mechanical waves), the relationship between wavelength and energy may be different.