Final answer:
A nonpolar molecule is formed when the molecular geometry allows for the symmetrical distribution of electrons and the cancellation of dipole moments. With identical atoms attached to the central atom, both linear and trigonal planar geometries would produce nonpolar molecules due to their symmetrical arrangement.
Step-by-step explanation:
To determine which molecular geometry produces a nonpolar molecule when all the atoms attached to the central atom are identical, we need to consider the symmetry of the molecule's electron distribution. A nonpolar molecule arises when the electron distribution is even and the dipole moments cancel each other out.
Out of the options provided:
- Linear: Molecules with a linear geometry have a 180-degree angle between the bonded atoms. When the outer atoms are the same, the molecule is nonpolar because the bond dipoles cancel each other out.
- Trigonal Planar: In trigonal planar molecules, the central atom is bonded to three identical atoms in the same plane at 120-degree angles. The molecule is nonpolar because of the symmetrical arrangement.
- Tetrahedral: While tetrahedral molecules also involve symmetrical arrangements, if there is a lone pair on the central atom (like the bent molecular geometry), the molecule could be polar due to an uneven electron distribution.
- Bent: Bent molecules (less than 180-degree bond angles) are usually polar because the dipole moments do not cancel out completely.
Therefore, assuming that all of the atoms attached to the central atom are identical, both linear and trigonal planar geometries would produce nonpolar molecules as their symmetry allows for the complete cancellation of dipole moments.