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A consequence of Wien's displacement law is that the wavelength at which the intensity per unit wavelength of the radiation produced by a black body has a local maximum or peak, , is a function only of the temperature: =, where the constant b, known as Wien's displacement constant, is equal to + 2.897 771 955 × 10 −3 m K. [31]
Using Wien's law, one finds a peak emission per nanometer (of wavelength) at a wavelength of about 500 nm, in the green portion of the spectrum near the peak sensitivity of the human eye. [3] [4] On the other hand, in terms of power per unit optical frequency, the Sun's peak emission is at 343 THz or a wavelength of 883 nm in the near infrared ...
The 41.8% point is the wavelength-frequency-neutral peak (i.e. the peak in power per unit change in logarithm of wavelength or frequency). These are the points at which the respective Planck-law functions 1 / λ 5 , ν 3 and ν 2 / λ 2 , respectively, divided by exp ( hν / k B T ) − 1 attain their maxima.
This equation is known as the Planck relation. Additionally, using equation f = c/λ, = where E is the photon's energy; λ is the photon's wavelength; c is the speed of light in vacuum; h is the Planck constant; The photon energy at 1 Hz is equal to 6.626 070 15 × 10 −34 J, which is equal to 4.135 667 697 × 10 −15 eV.
Meanwhile, the pressure is the rate of momentum change per unit area. Since the momentum of a photon is the same as the energy divided by the speed of light, u = T 3 ( ∂ u ∂ T ) V − u 3 , {\displaystyle u={\frac {T}{3}}\left({\frac {\partial u}{\partial T}}\right)_{V}-{\frac {u}{3}},} where the factor 1/3 comes from the projection of the ...
This equation may also be written as [3] [6] (,) =, where (,) is the amount of energy per unit surface area per unit time per unit solid angle per unit wavelength emitted at a wavelength λ. Wien acknowledges Friedrich Paschen in his original paper as having supplied him with the same formula based on Paschen's experimental observations.
The rate of spontaneous emission (i.e., the radiative rate) can be described by Fermi's golden rule. [17] The rate of emission depends on two factors: an 'atomic part', which describes the internal structure of the light source and a 'field part', which describes the density of electromagnetic modes of the environment.
Schwarzschild's equation is the formula by which you may calculate the intensity of any flux of electromagnetic energy after passage through a non-scattering medium when all variables are fixed, provided we know the temperature, pressure, and composition of the medium.