Wavelength, frequency, and photon energy are interconnected properties that describe different aspects of electromagnetic waves, including light. Here's an overview of their relation and differences:
Wavelength (λ): Wavelength is the distance between two consecutive peaks or troughs of a wave. It represents the spatial extent of one complete cycle of the wave. In the context of light, wavelength refers to the distance between successive peaks or troughs of the electromagnetic wave. Wavelength is typically measured in units such as meters (m), nanometers (nm), or angstroms (Å). The relationship between wavelength and frequency is inverse: longer wavelengths correspond to lower frequencies, and shorter wavelengths correspond to higher frequencies.
Frequency (ν): Frequency represents the number of complete cycles (or oscillations) of a wave that occur in one second. It indicates how many wave crests pass a given point per unit of time. Frequency is measured in units called hertz (Hz), which represent the number of cycles per second. Higher frequencies correspond to shorter wavelengths, and lower frequencies correspond to longer wavelengths.
Photon Energy (E): Photon energy refers to the energy carried by an individual photon, which is a quantum of electromagnetic radiation. The energy of a photon is directly proportional to its frequency (ν) and inversely proportional to its wavelength (λ). This relationship is described by the equation:
E = hν
where E represents the energy of a photon, h is Planck's constant (approximately 6.626 x 10^-34 joule-seconds), and ν is the frequency of the photon. This equation shows that photons with higher frequencies (shorter wavelengths) have higher energy, while photons with lower frequencies (longer wavelengths) have lower energy.
In summary, wavelength and frequency describe the properties of a wave, with wavelength referring to the spatial extent of the wave and frequency indicating the number of wave cycles per unit of time. Photon energy, on the other hand, is the energy carried by an individual photon and is directly proportional to its frequency and inversely proportional to its wavelength. The relationships can be summarized as: shorter wavelengths correspond to higher frequencies and higher photon energies, while longer wavelengths correspond to lower frequencies and lower photon energies.