$(20$ points total$).$ Consider the Morse potential given by

$U(R)=D[1-e^{-(R-R_0)}{]}^2$

Fix the three potential parameters as follows: $D=102\mathrm{.}5k\frac{J}{m}ol$;$=(\frac{1}{2\mathrm{.}85}){}^{-1},$ and $R_0=2\mathrm{.}1.$

a$)(5$ points$)$ Plot $U(R)$ as a function of $R,$ for $R=0$ to $R=12.$ Going out to $12$ will allow you to see the asymptotic behavior of the Morse function. Be sure to use enough points to generate a smooth curve.