I don't have the exam paper in front of me (and i am now leaving town for a few days so won't see it again for a bit). But I seem to recall that you had
lambda = hbar/(m c)
Was that correct? If so, this is also
lambda = fermi velocity / debye frequency
There are various ways this quantity can be important. I don't remember what in particular this question was asking. Probably, it was asking you to identify this as a "dephasing" length. For example, if an electron is in a "thermal" wavepacket (ie., its energy at the fermi surface is known up to the temperature unceratinty) then lambda = vf/T is the distance a "thermal" wavepacket moves before the phase of the wavepacket becomes completely unknown.