Nitrogen is gas while phosphorous, arsenic, antimony and bismuth are solid at room temperature because:

Nitrogen form $pπ-pπ$ multiple bond

The correct answer is Option (4) → Nitrogen form $pπ-pπ$ multiple bond.

The difference in physical states between nitrogen (gas) and the other elements of Group 15—phosphorus, arsenic, antimony, and bismuth (solids)—can be explained by differences in bonding and molecular structure, which arise due to their atomic size and electronic configurations.

Nitrogen's Small Size and Ability to Form Multiple Bonds

Small atomic size: Nitrogen has a very small atomic radius compared to phosphorus, arsenic, antimony, and bismuth. The smaller size allows for effective overlap of its \(2p\) orbitals, which facilitates the formation of strong \(p\pi −p\pi \) multiple bonds.

Triple bond formation \((N≡N)\): In diatomic nitrogen gas \((N_2)\), two nitrogen atoms are bonded by a triple bond, consisting of one \(\sigma \) bond and two \(\pi \) bonds formed by the sideways overlap of p orbitals. This strong triple bond is responsible for the stability and gaseous nature of nitrogen at room temperature. The energy required to break this bond is very high (~941 kJ/mol), making \(N_2\) a very stable gas.

Low intermolecular forces: Because nitrogen exists as discrete diatomic \(N_2\) molecules, the only forces between these molecules are weak van der Waals forces (London dispersion forces). These forces are not strong enough to hold the molecules together in a solid or liquid form at room temperature, so nitrogen remains a gas.

Larger Size of Heavier Group 15 Elements

As you move down Group 15, from phosphorus to bismuth, the atomic size increases significantly. Larger atomic size means that the valence orbitals (specifically the \(3p\), \(4p\), \(5p\), and \(6p\) orbitals) are more diffuse and less able to overlap effectively to form strong multiple bonds like nitrogen.

Single bond preference: Instead of forming strong π bonds (as nitrogen does with \(p\pi −p\pi \) overlap), phosphorus, arsenic, antimony, and bismuth prefer to form single bonds due to poor overlap of their p orbitals. These elements form \(P−P\), \(As−As\), \(Sb−Sb\), and \(Bi−Bi\) single bonds in solid structures, which are much weaker than the \(N≡N\) triple bond. These single bonds result in the formation of more complex network structures or lattices in the solid state, which are stabilized by strong covalent bonding.

Molecular Structure Differences

Nitrogen \((N_2)\): Exists as a simple diatomic molecule with a triple bond, which is a discrete, small gas molecule.

Phosphorus \((P_4)\): Exists as a tetrahedral \(P_4\) molecule in the solid state, where each phosphorus atom forms three single bonds with its neighbors. This molecular structure is held together by covalent bonds within the \(P_4\) units and weak van der Waals forces between the units.

Arsenic \((As)\), Antimony \((Sb)\), and Bismuth \((Bi)\): These elements tend to form network or layered structures in their solid forms, where atoms are covalently bonded to each other in a lattice. This extended bonding network increases the melting and boiling points, making these elements solids at room temperature.

Inability of Heavier Elements to Form \(\pi \) Bonds

The larger atomic size of phosphorus and the heavier elements in Group 15 prevents effective sideways overlap of p orbitals to form \(pi\) bonds. Hence, these elements cannot form stable multiple bonds like nitrogen can. 

The \(p\pi −p\pi \) overlap becomes inefficient as the atomic size increases. For phosphorus and the elements below it, the \(p\) orbitals are too large and diffuse to overlap sufficiently to form strong \(\pi \) bonds. This is why they form single bonds instead of multiple bonds.

Summary of the Bonding Trends

Nitrogen \((N_2)\) forms a strong triple bond through \(p\pi −p\pi \) multiple bonding due to its small size and effective orbital overlap. This leads to discrete molecules with weak intermolecular forces, making nitrogen a gas at room temperature.

Phosphorus, arsenic, antimony, and bismuth are larger atoms with poor p orbital overlap. They prefer to form single bonds and solidify into molecular or network structures with strong covalent bonds, resulting in solids at room temperature.

Thus, the key reason nitrogen is a gas at room temperature, while the others are solids, is that nitrogen forms \(p\pi −p\pi \) multiple bonds (specifically a triple bond in \(N_2\)), while the heavier elements cannot do so due to their larger atomic sizes and weaker orbital overlaps, leading them to form solid lattices or networks.