help with a potential energy curve problem?
The potential energy of a diatomic molecule (a two-atom system like H2 or O2) is given by
U= (A/r^12) - (B/r^6)
where r is the separation of the two atoms of the molecule and A and B are positive constants. This potential energy is associated with the force that binds the two atoms together.
(a) Find the equilibrium separation - that is, the distance between the atoms at which the force on each atom is zero. Is the force repulsive (atoms are pushed apart) or attractive (atoms are pulled together) if their separation is (b) smaller and (c) larger than the equilibrium separation?
I just need help on (b) and (c).
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If you can answer a) then you can answer b) and c). How did you calculate the equilibrium separation? Did you realize that the zero force corresponds to the minimum in the potential energy, which is how you calculate equilibrium based on energy arguments?
If the separation is smaller, they repel and viceversa. Look at the first derivative of U and its sign.
The force is found from the potential energy from;
F = - dU/dr
You find the equilibrium separation by solving F = 0 for "r". (in terms of A & B)
Next take the differential of the force;
dF = (dF/dr)dr
Evaluate (dF/dr) at the equilibrium "r" found above.
Then if dF is positive for positive dr you can conclude the force is repulsive as the separation increases beyond the equilbrium separation. If dF is negative then the force is attractive.
Then if dF is positive for negative dr you conclude the force is repulsive as the separation decreases from the equilibrium separation. If dF is negative then the force is attractive.
You can do the details, which appear to be lengthy.
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