= Solution
Using the given one-component equipartition estimate, $p^2=Mk_BT$. Substituting into the de Broglie relation gives
$$
\boxed{\lambda(T)\simeq\frac h{\sqrt{Mk_BT}}.}
$$
Comparison with a confinement <length> or interparticle spacing $d$ gives the criterion $T\lesssim h^2/(Mk_Bd^2)$. Numerical factors depend on the convention: the statistical <thermal de Broglie wavelength> is usually $h/\sqrt{2\pi Mk_BT}$, while a three-component root-mean-square <momentum> introduces a factor $\sqrt3$. The question's specified one-component convention is used consistently here. Once degeneracy becomes important, classical equipartition itself ceases to describe the <electrons> accurately.
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