The first systematic study on the mass dependence of the L-mode density limit is reported for JET H, D and T divertor plasmas. The density limit, defined as the density at the onset of the X-point MARFE, is found to scale inversely with the ion mass in vertical target configurations, while no isotope effect is found in horizontal target configurations. 2D numerical simulations reproduce the observed mass dependence in vertical target discharges. The experiments indicate a coupling between the mass and power dependence of the L-mode density limit. The experimental results are compared with analytic models, which suggest that the ion-neutral transverse collisionality plays a role in the density limit.