A new opacity model based on the Super-Transition-Array (STA) method for the calculation of monochromatic opacities of local thermodynamic equilibrium plasmas, was developed. The atomic code, named STAR (STA-Revised), is described and used to calculate spectral opacities for a solar model implementing the recent AGSS09 composition. Calculations are carried throughout the solar radiative zone. The relative contributions of different chemical elements and atomic processes to the total Rosseland mean opacity are analyzed in detail. Monochromatic opacities and charge state distributions were compared with the widely used Opacity-Project (OP) code, for several elements near the radiation-convection interface. STAR Rosseland opacities for the solar mixture show a very good agreement with OP and the OPAL opacity code, throughout the radiation zone. Finally, an explicit STA calculation of the full AGSS09 photospheric mixture, including all heavy metals was performed. It was shown that due to their extremely low abundance, and despite being very good photon absorbers, the heavy elements do not affect the Rosseland opacity.