In case of phosphorus, \(PCl_3\) and \(PCl_5\) are possible while nitrogen only forms \(NCl_3\), and not \(NCI_5\). This due to:

Nitrogen does not have vacant d-orbitals in its atom while phosphorus has vacant d-orbitals.

The correct answer is option 2. Nitrogen does not have vacant d-orbitals in its atom while phosphorus has vacant d-orbitals.

In \(PCl_3\) and \(PCl_5\), phosphorus forms covalent compounds with chlorine. Phosphorus can form \(PCl_3\) because it utilizes all three of its p-orbitals for bonding with three chlorine atoms, resulting in the formation of three σ bonds. In \(PCl_5\), phosphorus utilizes its three p-orbitals for bonding with three chlorine atoms, but it also has an empty d-orbital available for bonding with an additional chlorine atom, leading to the formation of five σ bonds.

In contrast, nitrogen does not have any available d-orbitals in its atom, so it cannot form compounds like \(NCl_5\) since it cannot exceed its maximum valency of 3 (using only its p-orbitals), leading to the formation of \(NCl_3\) instead.

Let's briefly discuss why the other options are incorrect:

1. Nitrogen is a gas while phosphorus is a solid at room temperature. The physical state of the elements (gas or solid) is not relevant to their ability to form compounds in this context.

3. The electronegativity of nitrogen is higher than that of phosphorus. Electronegativity differences do influence bonding characteristics, but they are not the primary reason for the difference in compound formation between nitrogen and phosphorus in this case.

4. The atom of nitrogen is smaller in size than phosphorus. Size differences may affect chemical properties, but in this context, the availability of d-orbitals for bonding is the crucial factor.