Question 188789
1.) A simple model for the mutual potential energy, V, of a pair of inert gas atoms is the Lennard-Jones function, {{{V=E(((a)/(r)^12)- 2((a)/(r)^6)))}}}, where r is the distance between the atonms and E and a are positive constants (E having units of energy, while a has units of distance).

a.) At what distance between the atoms is the potential enery a minimum?
{{{V = ar^-12 -2ar^-6}}}
{{{dV/dr = -12ar^-13 + 12ar^-7}}}
Set dV/dr = 0 to find min or max
{{{-12ar^-13 + 12ar^-7 = 0}}}
{{{12ar^-13 = 12ar^-7}}}
{{{r^-13 = r^-7}}}
Only 1 or zero satisfy this eqn.
r = 1 (units unknown)
r = 0 no potential energy when they're coincidental.
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I  looked up some info on Wikipedia and found that {{{V(r)=E (((r min)/(r)^12)- 2((rmin)/(r)^6))}}} 
F.Y.I.in the numerators r is regular size and 'min' is subscript.
then where {{{rmin=2^(1/6)a}}} is the distance at the minimum of the potential.

b.)What is the value of the potential energy?
If if i did the first part wrong, my answer  will be wrong here. Also, i don't know how to get a number value from the equation above...
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@ r = 1:
V = E*(a - 2a) = -Ea 
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