= Solution
For the <free electron model>, the \b[<Fermi energy> is the highest occupied one-electron <energy> at zero <temperature>], measured relative to the bottom of the free-electron band. The occupied <wavevectors> fill a disk in two dimensions or a sphere in three dimensions. The radius is the \b[<Fermi wavevector> $k_F$], with
$$
\boxed{E_F=\frac{\hbar^2k_F^2}{2m_e}.}
$$
Each allowed <wavevector> has two <spin> states. At nonzero <temperature>, the <Fermi-Dirac distribution> rounds the occupation boundary; the zero-temperature <Fermi energy> remains a useful density-defined scale and should not be defined as the thermal <energy> $k_{\rm B}T$.
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