Condensed matter - Is quantum effects relevant.

[dikmikkel]

a) Are quantum effects relevant for the air around us?

"Formulas":
The Fermi energy of athmosperic air:
[itex] \epsilon_F = \dfrac{\hbar^2}{2m_{air}}(3\pi^2C)^{2/3}[/itex]

Attempt to solve:
I calculated the fermi energy to : [itex] \epsilon_F = 1\times 10^{-25}\,\text{J}[/itex]
And [itex] k_bT = k_b 293\,\text{K} = 4\times 10^{-21}\,\text{J}[/itex]
The fermi energy is orders of magnutide smaller than kbT, and thus the quantum effects are not relevant.

Question:
What is the physical meaning of the term [itex] k_bT[/itex]

 

[BigJDubs]

? Answer:k_bT is the energy associated with a temperature of T, where k_b is Boltzmann's constant. It is a measure of the average energy of a system at that temperature, and thus can be used to determine whether quantum effects are relevant to a system.