PROBLEM $1$; For an ideal interaction potential between two ions, the energy $E($in $eV)$ is $E(r)=-\frac{2}{r^3}+\frac{0\mathrm{.}001}{r^8},$ where $r($in $nm)$ is the separation between the two ions. Calculate:

The equilibrium distance $r=r_0$

$2$

f$.0\mathrm{.}266nm$

g$.0\mathrm{.}308nm$

h$.0\mathrm{.}317nm$

i$.,0\mathrm{.}332nm$

j$.)0\mathrm{.}454nm$

The energy at $r_0,E(r_0)$

k$.)-20\mathrm{.}44eV$

$7.-39\mathrm{.}82eV$

m$.-58\mathrm{.}49eV$

n$.-66\mathrm{.}36eV$

o$.$ NoA

Find out the force $F$ in $N$ at $r_0$

p$.0\mathrm{.}00$

q$.1\mathrm{.}00$

r$.)18$

s$.$

t$.$ NoA

What would be the units of force that the formula directly produces?

u$.$ eV

v$.$ Joule$/$m

w$)$ Newton

x$.e\frac{V}{n}m$

y$.$ NoA

At what distance$($s$)$ is $E=0?$

z$.,0\mathrm{.}2459nm$ and $$

a$.0\mathrm{.}2187nm$ and $$

bb$.0$

cc$.r_0$ only

dd$.r_0$ and $$

At what distance$($s$)$ is $F=0?$

ee$.0\mathrm{.}2187nm$ and $$

ff$.0\mathrm{.}2459nm$ and $$

gg$.r_0$ only

hh$.r_0$ and $$

ii$.$ NoA