Answer the question on the basis of passage given below:
Nitrogen differs from rest of the members of group 15 due to its small size, high electronegativity, high ionization enthalpy and non-availability of d orbitals. Nitrogen has unique ability to form pл - рл multiple bonds with itself and with other elements having small size and high electronegativity. Heavier elements of this group do not form \(р\pi -р\pi \) bonds as their atomic orbitals are so large and diffuse that they cannot have effective overlapping.

Linear structure is exhibited by

\(N_2O\)

The correct answer is option 1. \(N_2O\).

Let us delve deeper into the molecular structures and geometries of each compound:

1. \( \text{N}_2\text{O} \) (Nitrous Oxide)

Nitrous oxide has a general structure that can be represented as

In the most common resonance structures, \( \text{N}_2\text{O} \) has a linear arrangement with a central nitrogen double-bonded to one terminal nitrogen and single-bonded to the terminal oxygen. Alternatively, it can also be described with the terminal nitrogen double-bonded to the oxygen.

Both representations lead to a linear structure because the molecule adopts a geometry that minimizes electronic repulsions in a linear arrangement.

The molecule exhibits linear geometry due to the arrangement of its bonds around the central nitrogen atom, which aligns the atoms in a straight line.

2. \( \text{NO}_2 \) (Nitrogen Dioxide)

Nitrogen dioxide has a central nitrogen atom double-bonded to one oxygen and single-bonded to another oxygen. The molecule also has an unpaired electron (radical) on the nitrogen. This results in a bent or V-shaped structure due to the lone pair on nitrogen, which creates a repulsive effect and forces the molecule into a bent geometry.

The lone pair on nitrogen and the two bonded oxygens result in a bond angle of approximately 134°, which is characteristic of a bent structure rather than a linear one.

3. \( \text{N}_2\text{O}_3 \) (Dinitrogen Trioxide)

Dinitrogen trioxide has a more complex structure involving two nitrogen atoms and three oxygen atoms. The structure can be described with two nitrogen atoms connected by a single bond and each nitrogen bonded to two oxygens, with some resonance structures involving N-O single and N=N double bonds. The presence of these bonds and lone pairs makes the structure non-linear.

The overall molecular geometry of \( \text{N}_2\text{O}_3 \) is not linear; instead, it has a more complex arrangement, often described as having a planar or bent structure depending on the resonance forms.

4. \( \text{N}_2\text{O}_4 \) (Dinitrogen Tetraoxide)

Dinitrogen tetraoxide is a dimer of \( \text{NO}_2 \) and involves a central N-N bond with each nitrogen bonded to two oxygen atoms. The molecule can be visualized as having a planar structure with the nitrogen atoms in the center and the oxygens arranged around them.

The N-N bond and the surrounding oxygens create a structure that is not linear. Instead, \( \text{N}_2\text{O}_4 \) has a planar, non-linear arrangement due to the bonding and lone pair effects.

Thus, the compound that exhibits a linear structure is \( \text{N}_2\text{O} \)