Thermal wavelength

This is often written in terms of the de Broglie thermal wavelength, A ... 

Question. At what temperature does the thermal wavelength of an argon atom become comparable to its diameter ... 

For free particles, the mean square radius of gyration is essentially the thermal wavelength to within a numerical factor, and for a ID harmonic oscillator in the oo limit. 

Expressions for the equation of state, de Broglie thermal wavelength, and rotational and vibrational partition functions for a diatomic molecule, provided by (28-87) and (28-89), as well as multiplication by Navo, allow one to determine the chemical potential on a molar basis. The final result for p, is consistent with its definition from classical thermodynamics ... 

The classical limit for the translational degrees of freedom is attained when < c 1, where p is the number density and is the momentum PF, or the de Broglie thermal wavelength. This... 

For small particles, inclusion of temperature effects related strictly to the particles oscillator modes is generally unnecessary whenever the thermal wavelength is much greater than the largest dimension of the particle, s (hc/kT) >> d. This is due to the inability of such a cavity (i.e., particle) to support all possible modes as does a body which is infinite in one or more dimensions [5.86]. However, the continuum-mode density must be included for those nonfinite media with which the particle interacts. Thus, for example, a 10 nm water particle near a water surface covered with lipid film (to use [5.85] chemical constituents) could respond to the thermal emissions of the lipid-water half-space as its electric susceptibility dictated, but it would have no thermal emissions of its own to contribute to the interaction energy of the system. 

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