The correct answer is A. linear.
In the VSEPR (Valence Shell Electron Pair Repulsion) theory, the molecular geometry is determined by the arrangement of electron pairs around the central atom. When a molecule has two atoms bonded to a central atom with no lone pairs on the central atom, it follows a linear geometry.
Linear geometry occurs when there are two bonding pairs and no lone pairs around the central atom. The two bonded atoms are positioned in a straight line, with a bond angle of 180 degrees. This arrangement minimizes the repulsion between electron pairs, leading to a linear molecular shape.
Therefore, option A. linear is the appropriate VSEPR shape for a molecule with two atoms bonded to a central atom and no lone pairs on the central atom.