We use Planck HFI data combined with ancillary radio data to study the emissivity index of the interstellar dust emission in the frequency range 100–353 GHz, or 3–0.8 mm, in the Galactic plane. We analyse the region l = 20°–44° and |b| ≤ 4° where the free-free emission can be estimated from radio recombination line data. We fit the spectra at each sky pixel with a modified blackbody model and two opacity spectral indices, βmm and βFIR, below and above 353 GHz, respectively. We find that βmm is smaller than βFIR, and we detect a correlation between this low frequency power-law index and the dust optical depth at 353 GHz, τ353. The opacity spectral index βmm increases from about 1.54 in the more diffuse regions of the Galactic disk, |b| = 3°–...