The scattering law S(k,w) for dilute polymer solutions is obtained from Kirkwood’s diffusion equation via the projection operator technique. The width Omega(k) of S(k,w) is obtained for all k without replacing the Oseen tensor by its average (as is done in the Rouse-Zimm model) using the "spring-bead" model ignoring memory effects. For small (ka root N much less than 1) and large (ka much greater than 1) values of k we find Omega = 0.195 k(2)/beta a eta(0) root N and Omega = k(2)/beta xi, respectively, indicating that the width is governed mainly by the viscosity eta(0) for small k values and by the friction coefficient xi for large k values. For intermediate k values which are of importance in neutron scattering we find that in the Rouse limit Omega = k(4)a(2)/12 beta xi. When the hydrodynamic effects are included, Omega(k) becomes 0.055 k(3)/beta eta(0). Using the Rouse-Zimm model, it is seen that the effect of pre-averaging the Oseen tensor is to underestimate the half-width Omega(k). The implications of the theoretical predictions for scattering experiments are discussed.