What Is the Distance at Which There Is No Net Force Between Two Atoms?

AI Thread Summary
To find the distance at which there is no net force between two atoms, the potential energy equation U(r) = 4Uatomic * [(r0/r)12 - (r0/r)6] is used. The net force is zero when the derivative of potential energy with respect to distance, F = -dU/dr, equals zero. By applying calculus, the correct distance can be determined using the given values of r0 and Uatomic. Once the distance is found, the potential energy at that position can also be calculated. This approach effectively resolves the problem of finding the equilibrium distance between the atoms.
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Homework Statement


The potential energy of two atoms separated by a distance r may be written as:

U(r) = 4Uatomic * [(r0/r)12 - (r0/r)6]

>Given r0 = 4.0 Ao and Uatomic = -0.012795 eV, what is the distance at which there is no net force between the atoms? Express your answer in terms of Ao.

>What is the potential energy at the position where the net force is 0 N? Express your answer in terms of eV.

Homework Equations


The above equation.


The Attempt at a Solution


I tried using Coulomb's Law, but I don't know the charges so it's not very helpful. Finding the total energy is also not relevant since I don't know mass or velocity. I'm pretty stuck here. I know once I find the first part I can find the second part easily, but I feel like I'm overlooking something simple for the first part of the question.
 
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Hint: What's the relationship between force and the potential function? (Use calculus.)
 
F = -dU/dr :) I tried it and it worked! Thanks for the hint!
 

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