We estimate the electron density, n_e, and its spatial variation in quiescent prominences from the observed emission ratio of the resonance lines Na i 5890 Å (D₂) and Sr ii 4078 Å. For a bright prominence (τ_{α}≈25) we obtain a mean n_e≈2×10^{10} cm^{-3}; for a faint one (τ _{α }≈4) n_e≈4×10^{10} cm^{-3} on two consecutive days with moderate internal fluctuation and no systematic variation with height above the solar limb. The thermal and non-thermal contributions to the line broadening, T_{kin} and V_{nth}, required to deduce n_e from the emission ratio Na i/Sr ii cannot be unambiguously determined from observed widths of lines from atoms of different mass. The reduced widths, Δλ_D/λ₀, of Sr ii 4078 Å show an excess over those from Na D₂ and Hδ 4101 Å, assuming the same T_{kin} and V_{nth}. We attribute this excess broadening to higher non-thermal broadening induced by interaction of ions with the prominence magnetic field. This is suggested by the finding of higher macro-shifts of Sr ii 4078 Å as compared to those from Na D₂.