$($a$)$ A metal has an atomic density $=6$x$1022/$cm$3,$ a resistivity $=2\mathrm{.}89106$cm and an electron mobility $=12$ cm$2/$Vs$.$ How many free electrons$/$atom are there for this metal? $($b$)$ What is the value of the mean free time $$ in silver if the resistivity $=1\mathrm{.}51106$cm$?($Given: Silver has $1$ free electron$/$atom; atomic weight$=107\mathrm{.}87$; mass density$=10\mathrm{.}49$ g$/$cm$3.$ N$.$B$.$ convert all units to SI$.)$