BCI3 is a planar molecule whereas NCI3 is pyramidal, because:

There are several factors that contribute to the molecular geometry of a molecule, including the nature of the bonding and the presence of lone pairs of electrons. In the case of BCI3 and NCI3, the key factor that differentiates their molecular geometries is the presence or absence of a lone pair of electrons.

1. B-Cl bond is more polar than N-Cl bond:
The polarity of a bond is determined by the difference in electronegativity between the two atoms involved. In the case of BCI3 and NCI3, both boron (B) and nitrogen (N) have similar electronegativities. However, chlorine (Cl) is more electronegative than both boron and nitrogen. Therefore, the B-Cl and N-Cl bonds in BCI3 and NCI3, respectively, are both polar. The difference in polarity between the two bonds does not explain the difference in molecular geometry.

2. N-Cl bond is more covalent than B-Cl bond:
Covalent bonds involve the sharing of electron pairs between atoms. The degree of covalency in a bond is determined by the electronegativity difference between the atoms. Since both B-Cl and N-Cl bonds involve the same chlorine atom, the electronegativity difference is not a contributing factor to the difference in molecular geometry between BCI3 and NCI3.

3. Nitrogen atom is smaller than boron atoms:
The size of an atom can influence its geometry by affecting the bond angles and the space available for other atoms or lone pairs. In the case of BCI3 and NCI3, boron is larger than nitrogen. However, the size difference does not explain the difference in molecular geometry between the two molecules.

4. BCI3 has no lone pair but NCI3 has a lone pair of electrons:
The key factor that determines the molecular geometry of BCI3 and NCI3 is the presence or absence of a lone pair of electrons on the central atom. In BCI3, boron does not have any lone pairs of electrons, allowing the three chlorine atoms to be arranged in a planar structure. On the other hand, nitrogen in NCI3 has one lone pair of electrons, which repels the chlorine atoms and forces them into a pyramidal arrangement.

In summary, the correct answer is option 'D' because the presence of a lone pair of electrons on the central nitrogen atom in NCI3 leads to a pyramidal molecular geometry, while the absence of a lone pair on the central boron atom in BCI3 allows for a planar molecular geometry.