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For example, the photons emitted by a radio station broadcast at the frequency ν = 100 MHz, have an energy content of νh = (1 × 10 8) × (6.6 × 10 −34) = 6.6 × 10 −26 J, where h is the Planck constant. The wavelength of the station is λ = c/ν = 3 m, so that λ/(2π) = 48 cm and the volume is 0.109 m 3.
is the speed of light (i.e. phase velocity) in a medium with permeability μ, and permittivity ε, and ∇ 2 is the Laplace operator. In a vacuum, v ph = c 0 = 299 792 458 m/s, a fundamental physical constant. [1] The electromagnetic wave equation derives from Maxwell's equations.
ω = 2πf is the angular frequency and frequency ... This last equation is in a very ... List of equations in nuclear and particle physics; List of equations in wave ...
The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy. Photon energy can be expressed using any energy unit.
For example, a wavenumber in inverse centimeters can be converted to a frequency expressed in the unit gigahertz by multiplying by 29.979 2458 cm/ns (the speed of light, in centimeters per nanosecond); [5] conversely, an electromagnetic wave at 29.9792458 GHz has a wavelength of 1 cm in free space.
The Planck relation [1] [2] [3] (referred to as Planck's energy–frequency relation, [4] the Planck–Einstein relation, [5] Planck equation, [6] and Planck formula, [7] though the latter might also refer to Planck's law [8] [9]) is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: =.
For example, in imperial units, the speed of light is approximately 186 282 miles per second, [Note 3] or roughly 1 foot per nanosecond. [Note 4] [16] [17] In branches of physics in which c appears often, such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where c = 1.
For example, in green light (with a wavelength of 555 nanometres or a frequency of 540 THz) each photon has an energy E = hf = 3.58 × 10 −19 J. That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules.