Final answer:
The polarity of a molecule with identical outer atoms depends on its molecular geometry; symmetrical geometries generally result in nonpolar molecules, while asymmetrical geometries, especially those with lone pairs on the central atom, are likely to be polar.
Step-by-step explanation:
To determine whether a molecule with identical outer atoms and a central atom with a different electronegativity is likely to be polar, you must consider the molecule's molecular geometry. If the molecular geometry is symmetrical, as in the case of a tetrahedral (e.g., methane, CH4) or trigonal planar (e.g., boron trifluoride, BF3) molecule, the molecule is typically nonpolar because the dipoles cancel out. However, if the molecule has a central atom with lone pairs, the geometry could be asymmetrical, leading to a polar molecule since the existence of lone pairs affects the electron-pair geometry and disrupts symmetry. Taking into account lone pairs is essential, as they can create dipole moments that result in a polar molecule, even with identical outer atoms.