Current density and drift velocity

[Parad0x88]

Homework Statement

1. A copper wire 2 mm in diameter carries a 4 A current. Determine the current density in the wire, drift velocity of the electrons and the mean time between collisions. Assume that each copper atom contributes one free electron. Hint: you may need some additional parameters of copper to solve this problem.

Homework Equations

A) For current density: J = I/A
We know: A = ∏r² m²

B) Drift velocity: I = nqV_dA . thus V_d = I / (nqA)
We know: n = density/mass atom, or (8.95g/cm³ X 10⁶ cm³/m³) / 1.05565 X 10^-22g/atom = 8.478 X 10²⁸ atoms/m³
q = 1.602 X 10^-19 C

C) σ = (nqτ²)/m^e, thus τ = σm_e / nq²
and σ = 1/p, p being resistivity, and resistivity for copper is 1.7 X 10^-8 ohm*m

The Attempt at a Solution

A) ∏*0.002²m² = 1.2265 X 10^-5 m²
4 / 1.2265 X 10^-5 = 318,309.89 A

B) Simply plug in the numbers: V_d = 4A / (8.478 X 10²⁸/m³ * 1.602 X 10^-19 C * 1.2265 X 10^-5 m² = 2.4012 X 10 ^-5 m/s

C) For C, I have no clue in which direction to go, I've browsed through my book but can't find any relevant formula

Any help for letter C would be appreciated, and also if you can check if what I did in A and B makes sense? Thank you!

Edit: I found something in the book, would the formula on C make sense?

 

[jbsteele]

τ = σme / nq2 = (1.7 X 10-8 ohm*m * 9.11 X 10-31 kg * 2.8 X 106 m/s)/(8.478 X 1028 atoms/m3 * 1.602 X 10-19 C2) = 8.068 X 10-15 s