SOLUTION: I started the problem, but not sure if i did it right and I'm not exactly sure what the question is asking me to do. I was given a formula and guessed how to get the answer. Any he

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Question 188789This question is from textbook Calculus:Early Transcendential Functions
: I started the problem, but not sure if i did it right and I'm not exactly sure what the question is asking me to do. I was given a formula and guessed how to get the answer. Any help is much appreciated!
Problem as stated on homework:
1.) A simple model for the mutual potential energy, V, of a pair of inert gas atoms is the Lennard-Jones function, V=E%5B%28%28a%29%2F%28r%29%5E12%29-+2%28%28a%29%2F%28r%29%5E6%29%29%5D, 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?
I looked up some info on Wikipedia and found that V%28r%29=E+%28%28%28r+min%29%2F%28r%29%5E12%29-+2%28%28rmin%29%2F%28r%29%5E6%29%29
F.Y.I.in the numerators r is regular size and 'min' is subscript.
then where rmin=2%5E%281%2F6%29a 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...
Thank you very much for any help! If anyone could please send this to me by the sometimes tonight. I have to turn it in by 3:15pm on monday. This question is from textbook Calculus:Early Transcendential Functions

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1.) A simple model for the mutual potential energy, V, of a pair of inert gas atoms is the Lennard-Jones function, V=E%28%28%28a%29%2F%28r%29%5E12%29-+2%28%28a%29%2F%28r%29%5E6%29%29%29, 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%5E-12+-2ar%5E-6
dV%2Fdr+=+-12ar%5E-13+%2B+12ar%5E-7
Set dV/dr = 0 to find min or max
-12ar%5E-13+%2B+12ar%5E-7+=+0
12ar%5E-13+=+12ar%5E-7
r%5E-13+=+r%5E-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%28r%29=E+%28%28%28r+min%29%2F%28r%29%5E12%29-+2%28%28rmin%29%2F%28r%29%5E6%29%29
F.Y.I.in the numerators r is regular size and 'min' is subscript.
then where rmin=2%5E%281%2F6%29a 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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