Diffusion length, $,$ is a popular term in characterizing the production of semiconductors by the controlled diffusion of impurities into a high$-$purity material. The value of $$ is taken as $2\sqrt[\phantom{2}]{Dt},$ where $$ represents the extent of diffusion for an impurity with a diffusion coefficient, $D,$ over a period of time, $t.$ Calculate the diffusion length for $B$ in $Ge$ for a total diffusion time of $30$ minutes at a temperature of $($a$)800C$ and $($b$)900C.$