# Confusion as to whether classical or quantum statistics be used [closed]

Suppose a gas is kept at a temperature of $$7000 \text{ K}$$ and has a particle density of $$2.7 \times 10^{34} \text m^{-3}$$. Do we need to treat it quantum mechanically or will classical treatment be sufficient for describing its dynamics?

• Classical treatment should be sufficient since, at such high temperatures, the quantum effects would effectively be classic (Fermi-Dirac or Bose-Einstein would tend to Boltzmann statistics) – exp ikx Oct 2 '19 at 10:03
• What are the units of particle density? – Amey Joshi Oct 2 '19 at 10:34
• That density is roughly 6 orders of magnitude greater than typical solid densities near STP. – Jon Custer Oct 2 '19 at 13:06

You haven't mentioned the unit of particle density. I assume that it is $$m^{-3}$$. In that case, the volume available to a single particle is $$10^{-34}/2.7$$. Equivalently, every particle is confined to a sphere of radius $$2.1 \times 10^{-12}$$ $$m$$, which is lesser than typical atomic size. Such a dense material needs a quantum mechanical treatment.