At room temperature the electrical conductivity and the electron mobility for copper are $6\mathrm{.}0$ x $107(-$m$)-1$ and $0\mathrm{.}0030$ m$2/$V$-$s$,$ respectively.

$($a$)$ Compute the number of free electrons per cubic meter for copper at room temperature.

$($b$)$ What is the number of free electrons per copper atom? Assume a density of $8\mathrm{.}9$ g$/$cm$3.$

$($atomic weight value for Cu$$viz$.63\mathrm{.}55$ g$/$mol$)$