- #1

I_Try_Math

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- Homework Statement
- The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by where $$U(x)=\frac {a} {x^{12}} - \frac {b} {x^6}$$ x is the distance between the atoms. (a) At what distance of separation does the potential energy have a local minimum (not at ∞ (b) What is the force on an atom at this separation? (c) How does the force vary with the separation distance?

- Relevant Equations
- $$U(x)=\frac {a} {x^{12}} - \frac {b} {x^6}$$

##U(x)=\frac {a} {x^{12}} - \frac {b} {x^6}##

##=ax^{-12} - bx^{-6}##

##U'(x)=-12ax^{-13} + 6bx^{-7}##

##-U'(x) = F(x) = 12ax^{-13} - 6bx^{-7}##

The answer for part (c) is supposedly x^6. If I found F(x) correctly then wouldn't the force drop to near zero as the distance gets larger? I can't see how it varies as x^6.

##=ax^{-12} - bx^{-6}##

##U'(x)=-12ax^{-13} + 6bx^{-7}##

##-U'(x) = F(x) = 12ax^{-13} - 6bx^{-7}##

The answer for part (c) is supposedly x^6. If I found F(x) correctly then wouldn't the force drop to near zero as the distance gets larger? I can't see how it varies as x^6.