C

To determine the effective range of nuclear forces, we need to analyze the order of magnitude typically associated with such interactions. Nuclear forces are significant at distances on the order of atomic sizes, generally around $10^{-15}$ m, which corresponds to the scale of protons and neutrons within an atomic nucleus. In this context, distances of $10^{-10}$ m and $10^{-13}$ m are more associated with chemical bonding and atomic interactions, whereas $10^{-20}$ m is significantly smaller than what we typically encounter in nuclear physics.
Therefore, the correct answer is that the effective nuclear forces occur at a distance of approximately $10^{-15}$ m.