Thermal de Broglie wavelength

The thermal de Broglie wavelength can be roughly described as the average de Broglie wavelength of particles in an ideal gas at a specified temperature. When compared to average inter-particle spacing in the gas, it can be used to tell if the gas can be considered to be a classical or Maxwell-Boltzmann gas, in which case the thermal wavelength must be much smaller than the average inter-particle spacing. Otherwise, quantum effects must be taken into account.

Notation:

  1. (hbar) is hbar.

  2. kB (k_B) is boltzmann_constant.

Links:

  1. Wikipedia, see last formula in paragraph.

thermal_wavelength

Thermal de Broglie wavelength of the gas.

Symbol:

lambda

Latex:

λ

Dimension:

length

mass

mass of a single gas particle.

Symbol:

m

Latex:

m

Dimension:

mass

temperature

temperature of the gas.

Symbol:

T

Latex:

T

Dimension:

temperature

definition

lambda = hbar * sqrt(2 * pi / (m * k_B * T))

Latex:
λ=2πmkBT