The quantity $k_{\rm F}=\frac{2\pi}{\lambda_{\rm F}}$ is called the _Fermi wavevector_, where $\lambda_{\rm F}$ is the _Fermi wavelength_, which is typically in the order of the atomic spacing.
The quantity $k_{\rm F}=\frac{2\pi}{\lambda_{\rm F}}$ is called the _Fermi wavevector_, where $\lambda_{\rm F}$ is the _Fermi wavelength_, which is typically in the order of the atomic spacing.
For copper, the Fermi energy is ~7 eV $\rightarrow$ thermal energy of the electrons ~70 000 K ! The _Fermi velocity_ $v_{\rm F}=\frac{\hbar k_{\rm F}}{m}\approx$ 1750 km/s $\rightarrow$ electrons run with a significant fraction of the speed of light, only because lower energy states are already filled by other electrons.
For copper, the Fermi energy is ~7 eV. It would take a temperature of $\sim 70 000$K for electrons to gain such energy through a thermal excitation! The _Fermi velocity_ $v_{\rm F}=\frac{\hbar k_{\rm F}}{m}\approx$ 1750 km/s $\rightarrow$ electrons run with a significant fraction of the speed of light, only because lower energy states are already filled by other electrons.
The total number of electrons can be expressed as $N=\frac{2}{3}\varepsilon_{\rm F}g(\varepsilon_{\rm F})$.
The total number of electrons can be expressed as $N=\frac{2}{3}\varepsilon_{\rm F}g(\varepsilon_{\rm F})$.
