The potential energy of a diatomic molecule (a two-atom system likeH2 or O2) is

Question

The potential energy of a diatomic molecule (a two-atom system likeH2 or O2) is given by
U= (A/r^12) - (B/r^6)where r is the separation of the two atoms ofthe molecule and A and B are positive constants. This potentialenergy is associated with the force that binds the two atomstogether.
(a) Find the equilibrium separation - that is, the distance betweenthe atoms at which the force on each atom is zero. Is the forcerepulsive (atoms are pushed apart) or attractive (atoms are pulledtogether) if their separation is (b) smaller and (c) larger thanthe equilibrium separation?
I an just not understanding this problem, any help would be a greathelp!

Explanation / Answer

F = - dU / dr So take the derivative of U and set it equal to zero to findequilibrium -dU/dr = 12 A / r13 - 6 B / r7 = 0= F Likewise dF / dr will show the direction of the force as r isincreased or decreased. Consider a weight being raised in a gravitational field As the weight is raised   F = -d (K / r) / dr = -K /r2   the force is directed downwards and goesto zero at infinity In the above problem the second derivative just gives thedirection of the rotation of the tangent to the potential energy curve which is the derivativeof the force and tells you if the force is increasing ordecreasing.

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