We show that various factors can lead to an isotopic dependence of the penetration depth $δ$. Non-adiabaticity (Jahn-Teller crossing) leads to the isotope effect of the charge carrier concentration $n$ and, consequently, of $δ$ in doped superconductors such as the cuprates. A general equation relating the isotope coefficients of $T_c$ and of $δ$ is presented for London superconductors. We further show that the presence of magnetic impurities or a proximity contact also lead to an isotopic dependence of $δ$; the isotope coefficient turns out to be temperature dependent, $β(T)$, in these cases. The existence of the isotope effect for the penetration depth is predicted for conventional as well as for high-temperature superconductors. Various experiments are proposed and/or discussed.

11 pages, 8 figures, accepted for publication in Phys. Rev. B