(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The potential energy of two atoms in a diatomic molecule is approximated by U(r)= ar[itex]^{-12}[/itex] - βr[itex]^{-6}[/itex], where is the spacing between atoms and α and β are positive constants.

From earlier parts of the equation, it has been that determined that force between two atoms as a function of r is

F(r)= 12ar[itex]^{-13}[/itex] - 6βr[itex]^{-7}[/itex].

and that the equilibrium distance between them r[itex]_{min}[/itex] is

[itex]\sqrt[6]{2α/β}[/itex]

Part a: Is the equilibrium stable? (My note: a stable equilibrium is a local minimum in a potential energy function. An unstable is a local maximum)

Part b:

Asssuming that the molecules are at said equlimbrium distance apart, find the energy required to bring the molecules an infiinite distance apart., and express this equation in terms of α and β

2. Relevant equations

W=∫ F dr= ΔU

3. The attempt at a solution

To part a:

Since potential energy is negatively related to displacement, and there are only two scenarios where Force could be 0 (at this distance or at infinity), I believe this equilibrium is unstable.

to part b:

∫[itex]^{∞}_{equilibrium}[/itex] (12ar[itex]^{-13}[/itex] - 6βr[itex]^{-7}[/itex]) dx

which appears to be negative infinity, which I'm fairly certain is wrong.

Part b is what's really giving me problems. I'm not sure exactly what I'm looking for; I've honestly never dealt with dissociation before. I considered integrating the potential energy function from 0 to infinity, but that would give me the wrong units. Perhaps I'm looking for an energy equal to the maximum potential energy possible with the function?

Any help would be greatly appreciated

Thanks in advance!

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# Dissociation energy of two particles-variables only equation-mastering physics

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