Cross sections for the vibrational excitation of molecular hydrogen and its five heavier isotopes by the impact of low energy electrons are calculated using both the local and the nonlocal versions of the resonance model. It is demonstrated that, for a given incident electron energy, the cross sections for the vibrational excitation of heavier isotopes can be obtained from those of molecular hydrogen by a simple scaling procedure. It is seen that the scaling law holds for cross sections with values ranging over eight orders of magnitude.