We present new unified theory line profiles of neutral Na perturbed by H_2_ . We used a priori NaH_2_ potentials, transition dipole moments and validated pseudo-potentials as input to the line shape, and evaluated the profiles for temperatures and densities appropriate for modeling exoplanet and brown dwarf atmospheres. The theory for the resonance lines was compared with new laboratory spectra of sodium to test the validity of the potentials and resulting profiles. The Lorentzian function commonly used to approximate a collisional line profile in radiative transfer calculations is shown to be inadequate, except within a few halfwidths of the line center. In the far wing, the opacity caused by collisions may be several orders of magnitude greater than the extrapolation of the Lorentzian core.