One can deduce quite a bit about intermolecular or interatomic forces just from a simple experiment, and from the observations that solid objects are difficult to compress and, once broken, do not spontaneously repair.
Take a short piece of metal wire (e.g. a straightened paper clip), and try to stretch it along its length. Unless the wire is very thin or you are very strong, the amount of stetching will be small, and the wire will not break. What has happened here is that you have slightly increased the average distance, r, between the atoms. However, the attractive force between pairs of atoms has been able to resist the tensile force you applied.
Now try to shorten the metal by exerting a compressive force along its length. Here, you have slightly decreased the average distance between the atoms but the repulsive force between pairs of atoms has been able to resist the compressive force you applied.
From this you can deduce that, (i) when the interatomic spacing is greater than its unstressed value, the attractive forces between atoms must be greater than the repulsive forces (the attractive forces balance both the repulsive forces and the forces you impose). Conversely, (ii) when the interatomic spacing is less than its unstressed value, the repulsive forces between atoms must be greater than the attractive forces.
Two further observations: First it is extremely difficult to compress a metal, so (iii) the repulsive forces must become very large, even for small reductions in r. Second, once you have broken a piece of metal, it doesn't automatically spring back together: (iv) if the atoms are separated from each other by even a distance of much less than a mm, the attractive forces are effectively zero.
From all these observations, we can deduce that the interatomic repulsive and attractive forces, as a function of interatomic separation must look qualitatively rather as shown in the graph below at left.
Again, a vertical grey line marks the unstressed value of r and, of course, it identifies the separation at which the total force is zero. This is also the point at which the potential energy U has a minimum, because the total force Fr = −dU/dr. (See potential energy.)
Our aim here is to relate these curves to Young's modulus and Hooke's law. But how can curves like these give a linear relation between the force applied and the stretching of the interatomic bonds? The answer is that Hooke's law only applies over a limited range of deformation. It corresponds to a linear approximation to F(r), passing through the point (r0,0), where r0 is the unstressed length. Integrating Hooke's law gives a potential energy U(r) that is parabolic about the minimu at r0. Hooke's law thus corresponds to the green linedrawn on the F(r) plot and the green parabola on the U(r) plot. The insets on each graph show close-ups of these approximation, and show that the approximations are poor for deformations of more than a few percent.
(While discussing this graph, let's observe that, although the Hooke's law approximation for U(r) is symmetrical about its minimum, these curves (and more realistic curves) are not. This asymmetry about the minimum in U(r) is responsible for the thermal expansion of (most) condensed phases: At finite temperatures, the atoms are not found exactly at the minimum of U, because they have finite kinetic energy due to their thermal motion. Oversimplifying in the interests of brevity, we can argue that the average value of U at a value above the minimum lies to the right of the minimum, and increases as more thermal energy is added.)