In physics, the thermal de Broglie wavelength (, sometimes also denoted by ) is roughly the average de Broglie wavelength of particles in an ideal gas at the specified temperature. We can take the average interparticle spacing in the gas to be approximately (V/N)1/3 where V is the volume and N is the number of particles. When the thermal de Broglie wavelength is much smaller than the interparticle distance, the gas can be considered to be a classical or Maxwell–Boltzmann gas. On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the interparticle distance, quantum effects will dominate and the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. The critical temperature is the transition point between these two regimes, and at this critical temperature, the thermal wavelength will be approximately equal to the interparticle distance. That is, the quantum nature of the gas will be evident for
i.e., when the interparticle distance is less than the thermal de Broglie wavelength; in this case the gas will obey Bose–Einstein statistics or Fermi–Dirac statistics, whichever is appropriate. This is for example the case for electrons in a typical metal at T = 300 K, where the electron gas obeys Fermi–Dirac statistics, or in a Bose–Einstein condensate. On the other hand, for
i.e., when the interparticle distance is much larger than the thermal de Broglie wavelength, the gas will obey Maxwell–Boltzmann statistics.[1] Such is the case for molecular or atomic gases at room temperature, and for thermal neutrons produced by a neutron source.
^Charles Kittel; Herbert Kroemer (1980). Thermal Physics (2 ed.). W. H. Freeman. p. 73. ISBN 978-0716710882.
and 25 Related for: Thermal de Broglie wavelength information
physicist Louis deBroglie (/dəˈbrɔɪ/) in 1924, and so matter waves are also known as deBroglie waves. The deBrogliewavelength is the wavelength, λ, associated...
classical limit to apply, a necessary condition is that the thermaldeBrogliewavelength, Λ = ( 2 π ℏ 2 m k B T ) 1 / 2 {\displaystyle \Lambda =\left({\frac...
of a system where the interparticle distance is equal to the thermaldeBrogliewavelength. Quantum effects become appreciable when the particle concentration...
n_{e}} is the electron density λ {\displaystyle \lambda } is the thermaldeBrogliewavelength of an electron λ = d e f h 2 2 π m e k B T {\displaystyle...
disturbing the structure. Given the equation for the deBrogliewavelength above, the same wavelength of a beam can be achieved at lower energies by using...
and wavelength of the neutron are related through the deBroglie relation. The long wavelength of slow neutrons allows for the large cross section. But...
\end{aligned}}} The quantity Λ {\displaystyle \Lambda } is the thermaldeBrogliewavelength of the particle, which enters due to the integration over the...
macroscopically occupied below a critical temperature — roughly when the thermaldeBrogliewavelength is longer than the interatomic spacing. Superfluidity in liquid...
where again, Lis(z) is the polylogarithm function and Λ is the thermaldeBrogliewavelength. Further results can be found in the article on the ideal Fermi...
likely to be, which itself is proportional to the neutron's thermaldeBrogliewavelength. λ ( E ) = h 2 m E {\displaystyle \lambda (E)={\frac {h}{\sqrt...
\right)^{\frac {1}{2}}}}\ /{\mbox{s}}} electron thermaldeBrogliewavelength, approximate average deBrogliewavelength of electrons in a plasma: λ t h , e = h...
T_{\text{e}})^{1/2}} [clarification needed] is the electron thermaldeBrogliewavelength. Otherwise, k max ∝ 1 / l C {\displaystyle k_{\text{max}}\propto...
fluids with particle velocities less than the speed of light and thermaldeBrogliewavelength smaller than the distance between particles. The theory is based...
{V}{\Lambda ^{3}}}} where Λ {\displaystyle \Lambda } is the thermaldeBrogliewavelength: Λ = h 2 2 π m k T {\displaystyle \Lambda ={\sqrt {\frac {h^{2}}{2\pi...
emission, notably by CH radicals emitting a wavelength band around 425 nm and is not seen in stars or pure thermal radiation). Atoms emit and absorb light...
holds throughout the quantum theory, including electrodynamics. The deBrogliewavelength λ of the particle is given by λ = h p , {\displaystyle \lambda ={\frac...
{\displaystyle E=m_{0}c^{2}} , deBroglie proposed that matter in motion appears to have an associated wave with wavelength λ = h / p {\displaystyle \lambda...
scattering. Achieving a precise velocity, i.e. a precise energy and deBrogliewavelength, of a neutron beam is important. Such single-energy beams are termed...
to the speed of light in vacuum, which is frequency-independent. For deBroglie matter waves the frequency dispersion relation is non-linear: ω ( k )...