The figure below shows the interatomic potential $($left panel$)$ and corresponding force

$($right$)$ for two fcc metals $($metal $1$ and metal $2).$ Assume that only nearest neighbor atoms

interact with one another $($i$.$e$.$ each atom only "sees" its $12$ nearest neighbors$).$

$1\mathrm{.}1$ What is the relationship between the separation corresponding to the minimum of the

interatomic bonding $r_{\text{m}\text{i}\text{n}}$ and the equilibrium separation between atoms $r_{eq}$ at $T=0K?$

$r_{\text{m}\text{i}\text{n}}=r_{eq}{r}_{\text{m}\text{i}\text{n}}>r_{eq}T=300K{r}_{\text{m}\text{i}\text{n}}=r_{eq}{r}_{\text{m}\text{i}\text{n}}>r_{eq}{r}_{\text{m}\text{i}\text{n}}$

$r_{\text{m}\text{i}\text{n}}=r_{eq}$

$r_{\text{m}\text{i}\text{n}}>r_{eq}$

$1\mathrm{.}3If$ the atomic mass $of$ metal $1is$ larger than that $of$ metal $2.$ Which metal has a higher

density? Briefly explain your answer.

$1\mathrm{.}4$ Which $of$ the two metals has the highest Young's modulus? Explain you answer.$r_{\text{m}\text{i}\text{n}}$

$r_{\text{m}\text{i}\text{n}}=r_{eq}$

$r_{\text{m}\text{i}\text{n}}>r_{eq}$

$1\mathrm{.}2$ How about $atT=300K?$

$r_{\text{m}\text{i}\text{n}}$

$r_{\text{m}\text{i}\text{n}}=r_{eq}$

$r_{\text{m}\text{i}\text{n}}>r_{eq}$

$1\mathrm{.}3If$ the atomic mass $of$ metal $1is$ larger than that $of$ metal $2.$ Which metal has a higher

density? Briefly explain your answer.

$1\mathrm{.}4$ Which $of$ the two metals has the highest Young's modulus? Explain you answer.