When do quantum mechanics effects become important in this case?

Question

Consider a free electron with energy E in a metal. At which energy do the quantum mechanics effects become important? When should I consider the electron as a wave and not as a particle?
I thought that the QM effects become important when the electron wave-length (h/p) is shorter than the spacing of the atoms in the lattice: is this correct?
EDIT The problem I am tackling is this: an high-energy ion enters into a slab of gold and produces by ionization an electron with energy E which moves in the material until it is reabsorbed or exits the slab. The question I am asking is: at which energy the produced electron must be considered as a wave and not as a particle?

Pieter · Answer

Your edit makes clear what this question is about. At first I thought that this was about the free-electron gas, where it is essential that the electron must be treated as a fermion.

When the electron has an energy more than a few $kT$ above the Fermi level, the Pauli exclusion principle does not matter. One can treat the electron as a charge interacting with the Fermi gas. A moving charge causes excitations of electrons (and also collective excitations like plasmons) and it will lose energy in that way.

At low energies, there may be interaction with the lattice (band structure effects) like for example Umklapp scattering.

When do quantum mechanics effects become important in this case?

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