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. \(\hbar\) (hbar) is hbar.

2. \(k_\text{B}\) (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:

\(\lambda\)

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:

\[\lambda = \hbar \sqrt{\frac{2 \pi}{m k_\text{B} T}}\]