Mean Free Path is the average distance that free or conduction electrons travel through copper wire between collisions with stationary atomic elements of the wire.
Take a copper wire of cross-sectional area 3×10-6 square meters with current of 10 Ampères. Density of copper is 8.95 grams per cubic centimeter. The atomic weight of copper is 63.5 grams per mole. One atomic mass of any substance contains AN or Avogadro's Number (6.02×1023) of atoms. The volume taken by 63.5 grams of copper equals 63.5 grams divided by 8.95 grams per cubic centimeter or 7.09 cubic centimeters.
If each copper atom gives one free electron to the wire, then obtain the carrier density n from (6.02×1023)/7.09 or 8.48×1022 electrons per cubic centimeter, which comes to 8.48×1028 electrons per cubic meter. To estimate the average time τ between collisions for electrons in copper wire at 20° Centigrade, write τ = (mass of electron) divided by [(carrier density)×(electron charge)2×(copper resistivity)] or τ = m/(nq2ρ) where ρ is 1.7×10-8 (ohm•meters) for the copper wire described above.
Then τ comes to (9.11×10-31 kg) ÷ [(8.48×1028 e-/m3)(1.6×10-19C)2(1.7×10-8 Ω•m)] or 2.5×10-14 seconds.
Finally, the mean thermal speed (or effective speed) for free electrons in copper is taken as 1.6×106 meters per second and the mean free path λ is given by veff × τ equal to (1.6×106)(2.5×10-14) or 4×10-8 meters equal to 40 nanometers (compared with atomic spacings of approximately 0.2 nanometers). Although the time between collisions is very short, the electrons travel about 200 atomic distances before colliding with an atom.
