Silicon has the diamond structure, atomic weight $28\mathrm{.}09,$ and a density of $2329k\frac{g}{m^3}.$

Young's modulus in the $[111]$ direction is $188$ GPa and the surface energy of the

$(111)$ plane is $1\mathrm{.}2\frac{J}{m^2}.$ i$)$ Estimate the spacing of the atomic planes in the $[111]$

direction, ao$.$ ii$)$ Estimate the theoretical strength of silicon on the $(111)$ plane.