If $$AB_4$$ molecule is a polar molecule, a possible geometry of $$AB_4$$ is:

A molecule is polar if the individual bond dipole moments do not cancel each other out. Highly symmetric molecular geometries cause these dipoles to cancel perfectly, resulting in a nonpolar molecule ($$\mu = 0$$).

Detailed Evaluation of Each Option:

• Option A: Square Pyramidal

  • An $$\text{AB}_4$$ molecule with a square pyramidal shape typically has a central atom with 4 bonding pairs and 1 lone pair ($$\text{AB}_4\text{E}$$ type, like $$\text{IF}_4^-$$).
  • The four $$\text{A--B}$$ bonds form a square base, and their horizontal dipole components cancel each other out. However, the vertical dipole component from the lone pair at the apex is not counterbalanced by any bond or lone pair opposite to it.
  • Result: The molecule has a net dipole moment ($$\mu \neq 0$$) and is polar. This is a possible geometry.



• Option B: Tetrahedral

  • A regular tetrahedral geometry ($$\text{AB}_4$$ type, like $$\text{CH}_4$$ or $$\text{CCl}_4$$) has a perfectly symmetrical distribution of identical surrounding atoms around the central atom.
  • The dipoles of all four identical bonds point toward the corners of a regular tetrahedron and cancel each other out exactly.
  • Result: Net dipole moment is zero ($$\mu = 0$$); the molecule is nonpolar.



• Option C: Rectangular Planar

  • In a rectangular planar geometry, the four surrounding atoms lie in a single plane at the corners of a rectangle.
  • The bond dipoles opposite to each other are equal in magnitude and directly opposite in direction ($$180^\circ$$ apart), leading to complete cancellation.
  • Result: Net dipole moment is zero ($$\mu = 0$$); the molecule is nonpolar.



• Option D: Square Planar

  • A square planar geometry ($$\text{AB}_4\text{E}_2$$ type, like $$\text{XeF}_4$$) places four identical bonds at $$90^\circ$$ angles to each other in a single plane, with two lone pairs positioned vertically opposite ($$180^\circ$$) to each other.
  • Both the bond dipoles and the lone pair dipoles cancel out perfectly due to the symmetric configuration.
  • Result: Net dipole moment is zero ($$\mu = 0$$); the molecule is nonpolar.

Conclusion:

Among the given arrangements, tetrahedral, rectangular planar, and square planar geometries are perfectly symmetrical and lead to a nonpolar molecule. Only a square pyramidal arrangement breaks this directional symmetry, resulting in a polar molecule.

Answer: Option A — Square pyramidal