The energy of a photon is directly proportional to its frequency, not its wavelength. This relationship is described by the equation E = hf, where E represents the energy of the photon, h is Planck's constant (a fundamental constant of nature), and f is the frequency of the photon.
The frequency and wavelength of a photon are related by the speed of light (c) through the equation c = λf, where c is the speed of light, λ represents the wavelength, and f is the frequency.
Combining these equations, we can express the energy of a photon in terms of its wavelength:
E = hf = hc/λ
From this equation, we can see that the energy of a photon is inversely proportional to its wavelength. As the wavelength of a photon increases, its energy decreases. This means that photons of shorter wavelengths (such as gamma rays, X-rays, and ultraviolet light) have higher energy compared to photons of longer wavelengths (such as visible light, infrared, and radio waves).
In summary, the energy of a photon is determined by its frequency, and since frequency and wavelength are inversely related, photons of different wavelengths have different energies.