$[4]$ Resistivity in the range $10-2$ to $102$cm is required for an electronic devices and circuits; this can be achieved by adding a controlled impurity to produce electronic imperfections. These are extrinsic semiconductors. Note that the atomic concentration of Si is $5$x$1022/$cm$3.$ Intrinsic carrier concentration in Si is $1\mathrm{.}0$x$1010/$cm$3.$ The electron and hole mobilities for this material are $0\mathrm{.}14$ and $0\mathrm{.}05$ m$2/$V$$s$,$ respectively. $($a$)$ Calculate the resistance value of a pure $($intrinsic$)$ Si with a volume of $1$ cm$3.($b$)$ Find the resistance value when the Si crystal is doped with one atom of arsenic $($As$)$ in $109$ Si atoms. $($c$)$ Find the resistance value when the Si crystal is doped with one atom of boron $($B$)$ in $109$ Si atoms. $($d$)$ Describe your opinions from the solutions obtained in $($a$)-($c$).$