The lennard-jones potential the lennard-jones potential, which is a good approximation for the potential energy of two neutral atoms or molecules with a separation r, can be given in several mathematical forms. the two most common versions are: (a) = { ) 12 − 2( ) 6 } (b) where e , s and r0 are constants. a) explain by calculations or by logical reasoning why ro can be called the ”equilibrium distance” of the two atoms (or molecules). b) similarly, explain why ε is called the ”depth of the potential well”. c) use the general result that force is the negative gradient of the potential , and calculate in one dimension to obtain two expressions of the force between the two atoms based on equations (a) and (b). d) use the expression of the force derived from equation (a) to find the “two distances” at which there is zero force between the molecules. call the shorter distance r0 and show that . e) show that with this value of ro, equation (b) can be converted into equation (a). f) use one of the expressions of the force derived in c) and perform exact calculations to show that the separation giving the maximum attractive force is always 11 % further away than the equilibrium distance, or written mathematically, rm = 1.11 ro. note that a much more realistic case than two atoms is to consider a tip approaching a semiinfinite plane. to model that mathematically, one can assume that each pair of atoms in the tip and the sample interacts via a lennard-jones potential. it is relatively easy to show that also in this case, there will be an equilibrium distance r0. for r < r0, there is strong repulsion, and