## Wednesday, October 2, 2013

### thermal wavelength

can you estimate the thermal wavelength of hydrogen atoms today? assume that there's no additional heat input so that you can predict the atom's temperature from the CMB temperature. are the atoms classical or does one have to use a quantum mechanical description?

#### 1 comment:

1. the thermal wavelength, i.e. the de Broglie-wavelength of a particle whose kinetic energy is determined by equilibration, reads

\lambda = \frac{h}{\sqrt{2\pi mk_BT}}

and substituting numbers one obtains $\lambda\simeq10^{-10}$ meters, small compared to the typical distance between atoms, which is a few centimeters. the situation is very different for photons, whose thermal wavelength today is about a millimeter, similar to the typical "distance".