The force between two inert gas atoms is often described by a function of the form                                   F = [Ax^−13 + Bx^−7] ex where A and B are positive constants and x is the distance between the atoms. The origin has been placed at the location of one of the atoms, and F is the force on the other atom; ex points from the origin towards the other atom. Answer in terms of A and B.

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The force between two inert gas atoms is often described by a function of the form
                                  F = [Ax^−13 + Bx^−7] ex
where A and B are positive constants and x is the distance between the atoms. The origin has been placed at the location of one of the atoms, and F is the force on the other atom; ex points from the origin towards the other atom. Answer in terms of A and B.

(a) Plot the component of F as a function of x. For which values of x is this an attractive force, and for what values is this a repulsive force?

(b) What is the equilibrium separation?

(c) What is the work done if the atoms are moved from their equilibrium separation to a very large distance apart?

(d) Is this a conservative force? If yes, show it! If no, explain.

(e) Find the potential energy function (if applicable). Plot this function versus x.

(f) Explain the relation between your answers to parts b and d.

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