At room temperature the electrical conductivity and the electron mobility for copper are $6\mathrm{.}010^7($m$)1$and $0\mathrm{.}0030$ m$2/$Vs$,$ 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$3.$