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Photon energy is the energy carried by a single photon. 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.
To calculate the energy in the box in this way, we need to evaluate how many photon states there are in a given energy range. If we write the total number of single photon states with energies between ε and ε + dε as g ( ε ) dε , where g ( ε ) is the density of states (which is evaluated below), then the total energy is given by
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: =.
By applying the differentials to the energy equation and identifying the relativistic momentum: = then integrating, de Broglie arrived at his formula for the relationship between the wavelength , λ , associated with an electron and the modulus of its momentum , p , through the Planck constant , h : [ 14 ] λ = h p . {\displaystyle \lambda ...
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and v p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation .
In 1890, Rydberg proposed on a formula describing the relation between the wavelengths in spectral lines of alkali metals. [2]: v1:376 He noticed that lines came in series and he found that he could simplify his calculations using the wavenumber (the number of waves occupying the unit length, equal to 1/λ, the inverse of the wavelength) as his unit of measurement.
The Planck constant, or Planck's constant, denoted by , [1] is a fundamental physical constant [1] of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum.
The radius of the quantum dot affects the wavelength of the emitted light due to quantum confinement, and this equation describes the effect of changing the radius of the quantum dot on the wavelength λ of the emitted light (and thereby on the emission energy ΔE = hc/λ, where c is the speed of light). This is useful for calculating the ...