Lattice mismatch in core/shell nanoparticles occurs when the core and shell materials have different lattice parameters. When there is a significant lattice mismatch, a coherent core-shell interface results in substantial lattice strain energy, which can affect the shell morphology. The shell can be of uniform thickness or can be rough, having thin and thick regions. A smooth shell minimizes the surface energy at the expense of increased lattice strain energy and a rough shell does the opposite. A quantitative treatment of the lattice strain energy in determining the shell morphology of CdSe/CdS core/shell nanoparticles is presented here. We use the inhomogeneity in hole tunneling rates through the shell to adsorbed hole acceptors to quantify the extent of shell thickness inhomogeneity. The results can be understood in terms of a model based on elastic continuum calculations, which indicate that the lattice strain energy depends on both core size and shell thickness. The model assumes thermodynamic equilibrium, i.e., that the shell morphology corresponds to a minimum total (lattice strain plus surface) energy. Comparison with the experimental results indicates that CdSe/CdS nanoparticles undergo an abrupt transition from smooth to rough shells when the total lattice strain energy exceeds about 27 eV or the strain energy density exceeds 0.59 eV/nm(2). We also find that the predictions of this model are not followed for CdSe/CdS nanoparticles when the shell is deposited at very low temperature and therefore equilibrium is not established.