The graph of the Lennard-Jones potential energy between two particles is shown b

Question

The graph of the Lennard-Jones potential energy between two particles is shown below. A scientist uses a device to measure the kinetic energy between two particles. She measures the kinetic energy to be 0.4 elementof at a particle separation of r = 1.2 sigma. a.) What is the total energy of the system? b.) What is the minimum separation distance between the particles? is there a maximum separation distance? If so, what is it? c.) Draw, accurately, the kinetic energy and the total energy of this system on the above graph.

Explanation / Answer

A) total energy = KE+PE

= 0.4E - 0.9E

= - 0.5E

B) minimum and maximum separation will be when PE = - 0.4E so that total energy is zero.

Minimum separation = 1.0 sigma

Maximum separation =1.45 sigma

C) total energy = constant = - 0.5E

but the graph will be between 1.0 sigma and 1.45 sigma

Kinetic energy = - 0.5E - PE

SO KE will be maximum (-0.5E+1.0E = 0.5E) at r =1.2sigma

KE = 0 at 1.0 sigma and 1.45 sigma, graph will be between these two points only

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