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

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$12$ 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 $g_{?}=2\mathrm{.}165\frac{g}{c}{m}^3!$ The molar mass of $Na$ is $23\frac{g}{m}ol,$ that of chlorinc is $35\mathrm{.}4\frac{g}{m}ol.$ Avogarlio's constant $($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 between next$-$nearest 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 $C_H=12\mathrm{.}75$GPa. Use these values to calculate $(100$:$\})!$ Compare this value to your estimate!