$2$ Bonding Energy $[10$ points$]$

The potential energy between two adjacent ions, $K^{+}$and $C{l}^{-},$ is represented by the sum of the attractive and repulsive energies:

$E_N=-\frac{1\mathrm{.}436}{r}+\frac{5\mathrm{.}86{10}^{-6}}{r^9}.$

where $E_N^{}$ is the total energy $($in eV $)$ and r is the distance between ion centers $($in nm $).$ You can assume that the onstants in the equation will give you the correct units.

a$.$ Using your favorite plotting software, superimpose $E_N,E_A,$ and $E_R$ as a function of r up to $1\mathrm{.}0$ nm $.$ Be sure to label the axes as well as each potential energy curve. $[4$ points$]$

b$.$ Graphically determine the equilibrium spacing and the magnitude of the bonding energy between $K^{+}$and $C{l}^{-}.$ Briefly describe how you determined these values from your plot. $[3$ points$]$

c$.$ Mathematically calculate the equilibrum spacing and bonding energy, and compare to your graphical results from part $($b$).[3$ points$]$