We study the modification of the classical criterion for the linear onset
and growth rate of the Rayleigh-Taylor instability (RTI) in a partially ionized
(PI) plasma in the one-fluid description, considering a generalized induction
equation. The governing linear equations and appropriate boundary conditions,
including gravitational terms, are derived and applied to the case of the RTI
in a single interface between two partially ionized plasmas. The boundary
conditions lead to an equation for the frequencies in which some of them have
positive complex parts, marking the appearance of the RTI. We study the
ambipolar term alone first, extending the result to the full induction
equation later. The configuration is always unstable because of the presence of a neutral species. In the classical stability regime the growth rate is small, since the collisions prevent the neutral fluid to fully develop the RTI. For
parameters in the classical instability regime the growth rate is lowered,
but for the considered theoretical values of the collision frequencies and
diffusion coefficients for solar prominences the differences with the
compressible MHD case are small. We conclude that PI modifies some aspects of the linear RTI instability, since it takes into account that neutrals do not feel the stabilizing effect of the magnetic field. For the set of parameters representative for solar prominences, our model gives the resulting timescale comparable with observed lifetimes of RTI plumes.