Copper is FCC with a cubic edge $($lattice constant$)$ of $0\mathrm{.}36$ nm$,$ and each atom contributes one conduction electron. For bulk copper, the measured resistivity is $1\mathrm{.}6$ x $10-8\backslash$Omega $-$m$.$ The resistivity increases to $2\mathrm{.}1$ x $10-8\backslash$Omega $-$m as the copper is patterned to form interconnect lines with cross$-$sectional area $($line width x thickness$)$ of $22$ x $150$ nm$2.$ Assume the effective electron mass is equal to free electron mass. Estimate the relaxation $($or mean collision$)$ time of conduction electrons in the fine copper lines due to surface scattering