# (solution) 2. The Lennard-Jones potential describes the interaction

2. The Lennard-Jones potential describes the interaction potential between two particles as a function of

their separation distance r, and is given by:

V(r) = 4 ? [(?/r)12 – (?/r)6]

Assume that this potential also describes the interaction between an AFM cantilever tip and a surface, with the following interaction parameters:

? = 2e-20 J and ? = 0.5 nm

and that the force between the cantilever tip and the surface is given by F = -dV/dr.

1. Calculate the separation distance between the tip and the cantilever beam when the force is zero. (Hint: The force will be zero when the tip is infinitely far away and also at another, closer, separation distance. Find the non-infiniteanswer).
2. If the afm cantilever beam has a spring constant of 0.1 N/m, calculate the deflection of the cantilever beam at a separation distance of 0.5 nm. Indicate in a sketch the direction that the cantilever beam isbent

own), and justify your sketch.