Q $2($a$)[9$ Marks$]$ Find the maximum resistance of a rectangular block of germanium with the dimensions $10$ mm x $1$ mm x $2$ mm if it can be connected between any pair of parallel faces. Assume there are $1021$ m$-3$ mobile electrons, and the electron mobility in germanium is $0\mathrm{.}39$ m$2$V$-1$s $-1.$ Q $2($b$)[12$ Marks$]$ At low temperature, the resistivity produced by a given number of impurity ions in a metal is proportional to $($Z$)2,$ where $$Z is the difference in valency of the impurity from the host metal. A sample of copper has a resistivity of $10-10$m$.$ When it is alloyed with $0\mathrm{.}1$ atomic percent of Cd the resistivity increases to $5$x$10-10$m$.$ Using the respective valences, estimate the resistivity of alloys of copper alloyed with $0\mathrm{.}1$ atomic percent of $($a$)$ In and $($b$)$ Sn$?$ Explain your reasoning in each case. Q $2($c$)[9$ Marks$]$ Consider each of the following $3$ statements. In each case, highlight whether the statement is true or false and give reasons supporting your answers: $($i$)$ An intrinsic material in which the outer energy band is half full will be a conductor. $($ii$)$ The Fermi level for a heavily doped p$-$type or n$-$type semiconductor is midway between the top of the valence band and the bottom of the conduction band. $($iii$)$ Hole conductivity results in silicon when some of the silicon atoms are