Using the Lennard$-$Jones potential with $n=8{10}^{22}$ atom $/c{m}^3$ and ${}_b=0\mathrm{.}6eV/$ atom, $a_0=(\frac{1}{n}{)}^{\frac{1}{3}}$

$($a$)$ Calculate the maximum force $F_{\text{m}\text{a}\text{x}}.$

$($b$)$ Assume the solid is in the linear elastic region and calculate Young's mod$-$

ulus $Y.$

$($c$)$ What is the elastic energy $E_{\text{e}\text{l}\text{a}\text{s}\text{t}\text{i}\text{c}}$ at $F_{\text{m}\text{a}\text{x}}?$