$(2$ points$)$ What is the ratio between the shear stresses required for the $\frac{111}{110}$ and $(100)/\frac{1}{b}ar(1)1$ slip systems in aluminum? Assume $k$ in the Peierls$-$Nabarro stress equation is $2.$ The lattice parameter for aluminum is $0\mathrm{.}404958$ nm $.$

$($a$)\frac{{}_{\frac{111}{110}}}{{}_{\frac{110}{\frac{1}{b}ar(1)}}}$

$($b$)\frac{{}_{\frac{11}{110}}}{{}_{\frac{110}{111}}}$

$($c$)\frac{{}_{(111)[110]}}{{}_{\frac{110}{111}}}=0\mathrm{.}2863$

$($d$)\frac{{}_{\frac{111}{110}}}{{}_{\frac{110}{\frac{1}{b}ar(1)}}}=2\mathrm{.}259$

$($e$)$ None of the above