“Planck’s radiation law”的概念、定义、翻译、参考文献-科学参考

Planck’s radiation law

Physics

A law stated by Max Planck in 1900 giving the distribution of energy radiated in by a black body. It introduced into physics the novel concept of energy as a quantity that is radiated by a body in small discrete packets rather than as a continuous emission. These small packets became known as quanta and the law formed the basis of quantum theory. The Planck formula gives the energy radiated per unit time at frequency ν‎ per unit frequency interval per unit solid angle into an infinitesimal cone from an element of the black-body surface that is of unit area in projection perpendicular to the cone’s axis. The expression for this monochromatic specific intensity I_ν‎ is

$I_{ν} = 2 h c^{- 2} ν^{3} / [exp (h ν / k T - 1)],$

where h is the Planck constant, c is the speed of light, k is the Boltzmann constant, and T is the thermodynamic temperature of the black body. I_ν‎ has units of watts per square metre per steradian per hertz (W m⁻² sr⁻¹ Hz⁻¹). The monochromatic specific intensity can also be expressed in terms of the energy radiated at wavelength λ‎ per unit wavelength interval; it is then written as I_λ‎, and the Planck formula is

$I_{λ} = 2 h c^{2} λ^{- 5} / [exp (h c / λ k T) - 1] .$

There are two important limiting cases of the Planck formula. For low frequencies ν‎ << kT/h (equivalently, long wavelengths λ‎ >> hc/kT) the Rayleigh–Jeans formula is valid:

$I_{ν} = 2 c^{- 2} ν^{2} k T,$

or

$I_{λ} = 2 c λ^{- 4} k T,$

Note that these expressions do not involve the Planck constant. They can be derived classically and do not apply at high frequencies, i.e. high energies, when the quantum nature of photons must be taken into account. The second limiting case is the Wien formula, which applies at high frequencies ν‎ >> kT/h (equivalently, short wavelengths λ‎ << hc/kT):

$I_{ν} = 2 h c^{- 2} ν^{3} exp (- h ν / k T),$

or

$I_{λ} = 2 h c^{2} λ^{- 5} exp (- h c / λ k T) .$

See also Wien’s displacement law.

单词	Planck’s radiation law
释义	Planck’s radiation law Physics A law stated by Max Planck in 1900 giving the distribution of energy radiated in by a black body. It introduced into physics the novel concept of energy as a quantity that is radiated by a body in small discrete packets rather than as a continuous emission. These small packets became known as quanta and the law formed the basis of quantum theory. The Planck formula gives the energy radiated per unit time at frequency ν‎ per unit frequency interval per unit solid angle into an infinitesimal cone from an element of the black-body surface that is of unit area in projection perpendicular to the cone’s axis. The expression for this monochromatic specific intensity I_ν‎ is $I_{ν} = 2 h c^{- 2} ν^{3} / [exp (h ν / k T - 1)],$ where h is the Planck constant, c is the speed of light, k is the Boltzmann constant, and T is the thermodynamic temperature of the black body. I_ν‎ has units of watts per square metre per steradian per hertz (W m⁻² sr⁻¹ Hz⁻¹). The monochromatic specific intensity can also be expressed in terms of the energy radiated at wavelength λ‎ per unit wavelength interval; it is then written as I_λ‎, and the Planck formula is $I_{λ} = 2 h c^{2} λ^{- 5} / [exp (h c / λ k T) - 1] .$ There are two important limiting cases of the Planck formula. For low frequencies ν‎ << kT/h (equivalently, long wavelengths λ‎ >> hc/kT) the Rayleigh–Jeans formula is valid: $I_{ν} = 2 c^{- 2} ν^{2} k T,$ or $I_{λ} = 2 c λ^{- 4} k T,$ Note that these expressions do not involve the Planck constant. They can be derived classically and do not apply at high frequencies, i.e. high energies, when the quantum nature of photons must be taken into account. The second limiting case is the Wien formula, which applies at high frequencies ν‎ >> kT/h (equivalently, short wavelengths λ‎ << hc/kT): $I_{ν} = 2 h c^{- 2} ν^{3} exp (- h ν / k T),$ or $I_{λ} = 2 h c^{2} λ^{- 5} exp (- h c / λ k T) .$ See also Wien’s displacement law.
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