Concept: Molecular Geometry and Hybridization

The coplanarity of atoms in a molecule depends on its molecular geometry, which is determined by the hybridization of the central atom and the presence of lone pairs.

Why (B) is correct:

Let's analyze the geometry of each molecule:

• A) ${\mathrm{CH}}_4$ (Methane): The central carbon atom is ${\mathrm{sp}}^3$ hybridized, and there are no lone pairs. Its geometry is tetrahedral. In a tetrahedral structure, only three atoms (one central and two peripheral) can lie in the same plane at a time. Therefore, all five atoms are not coplanar.
• B) ${\mathrm{BF}}_3$ (Boron trifluoride): The central boron atom is ${\mathrm{sp}}^2$ hybridized, and there are no lone pairs. Its geometry is trigonal planar. In a trigonal planar structure, all four atoms (one central boron and three fluorine atoms) lie in the same plane. Thus, all atoms are coplanar.
• C) ${\mathrm{PF}}_3$ (Phosphorus trifluoride): The central phosphorus atom is ${\mathrm{sp}}^3$ hybridized, and it has one lone pair. Its geometry is trigonal pyramidal. In a trigonal pyramidal structure, the central atom is above the plane formed by the three peripheral atoms, so all atoms are not coplanar.
• D) ${\mathrm{NH}}_3$ (Ammonia): The central nitrogen atom is ${\mathrm{sp}}^3$ hybridized, and it has one lone pair. Its geometry is trigonal pyramidal. Similar to ${\mathrm{PF}}_3$, all atoms are not coplanar.

Option Analysis:

• A) ${\mathrm{CH}}_4$: Tetrahedral geometry, not coplanar.
• B) ${\mathrm{BF}}_3$: Trigonal planar geometry, all atoms are coplanar.
• C) ${\mathrm{PF}}_3$: Trigonal pyramidal geometry, not coplanar.
• D) ${\mathrm{NH}}_3$: Trigonal pyramidal geometry, not coplanar.

Correct Answer: (B)