The potential energy of a diatomic molecule is given as U = (a)/(x^(12)) - (b)/(x^(6)). Find the (i) stable equilibrium distance of separation between two atoms, (ii) force on each atom as the function of separating distance x.

The potential energy of a diatomic molecule is given as U = (a)/(x^(12

1.	The potential energy of a diatomic molecule is given as U = (a)/(x^(12)) - (b)/(x^(6)). Find the (i) stable equilibrium distance of separation between two atoms, (ii) force on each atom as the function of separating distance x.
Answer» SOLUTION :(i) LET us assume that the stable equilibrium separation between the atoms is `x_(0)`, where the potential energy U is miniumum. To find `x_(0)`, we take the derivative of U and equate it to zero , That MEANS `(dU)/(dx) = 0` where `U = (a)/(x^(12)) - (B)/(x^(6))` Then, we have `- (12 a)/(x_(0)^(13)) + (6b)/(x_(0)^(7)) = 0` This gives `x_(0) = ((2a)/(b))^(1//6)` (ii) The force between the atoms at any value of x is `F = - (dU)/(dx) = - (d)/(dx) ((a)/(x^(12))-(b)/(x^(6))) = (12A)/(x^(13)) - (6b)/(x^(7))`.