Exercise $3$: Interaction between two atoms

Assume the following functions for the interaction energy between two atoins of a molecule of commion salt $(NaCl)$ :

$40812$ Exercises

$U_A=-\frac{1\mathrm{.}436}{r}$eVnm,$U_R=\frac{5\mathrm{.}86{10}^{-6}}{r^9}eVn{m}^9.$

a$)$ Calculate the bond length of the diatomic molecule!

b$)$ How large is the binding energy?

c$)$ Compare the result of the calculation with the interatomic distance calculated for a NaCl crystal with a density of $=2\mathrm{.}165\frac{g}{c}{m}^3!$ The molar mass of $Na$ is $23\frac{g}{m}ol,$ that of chlorine is $35\mathrm{.}4\frac{g}{m}ol.$ Avogadro s coustant $($the number of molecules in a mol$)$ is $N_A=6\mathrm{.}022{10}^{23}mo{l}^{-1}.$

d$)$ Estimate Young's modulus of NaCl in the $($:$100$:$)$ direction! Neglect the bonds bet ween next$-$neruest ncighbours and those cven further away! Note: $1eV=1\mathrm{.}602{10}^{-19}J$

e$)$ The elastic constants of NaCl are $C_{11}=48\mathrm{.}7$GPa,$C_{12}=12\mathrm{.}6$GPa and $C_{44}=12\mathrm{.}75$GPa. Use these values to calculate $E_{(\text{:}100)}!$ Compare this value to your estimate!