Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 4 / d / ii

For two equal spheres of radius $R$, the effective radius in the Derjaguin approximation is $R_{\mathrm{eff}}=R/2$. The nonretarded attractive van der Waals potential isDifferentiating with respect to the surface gap givesThus the requested approximation gives an attraction of about $8.3$ pN. Here $h/R=2$, whereas the Derjaguin approximation requires $h\ll R$. This is the formal estimate requested by the hint, not a quantitatively reliable near-contact approximation for the printed dimensions.