Which of the following species has a linear shape?

To determine which species has a linear molecular shape, we examine the electron‑pair geometry of each candidate using VSEPR (Valence Shell Electron Pair Repulsion) theory.

1. Na₂⁻ (hypothetical di‑sodium anion):
- Each Na atom contributes one valence electron, and the extra electron gives a total of 3 electrons.
- This would result in a bond order less than 1 and a bent or angular arrangement, not linear.

2. SO₂:
- Sulfur has 6 valence electrons; each oxygen contributes 6 electrons, giving a total of 18 electrons (9 pairs).
- Two S–O bonds and one lone pair on sulfur lead to a trigonal planar electron geometry, resulting in a bent molecular shape.

3. NO₂⁺:
- Nitrogen has 5 valence electrons, each oxygen 6, and the positive charge removes one electron.
- Total electrons = 5 + (2 × 6) – 1 = 16 electrons (8 pairs).
- The arrangement is: two N–O bonds and no lone pairs on nitrogen.
- With two bonding pairs and zero lone pairs, the electron‑pair geometry is $linear$, giving a linear molecular shape.

4. O₃ (ozone):
- Three oxygen atoms share 6 valence electrons each, for a total of 18 electrons (9 pairs).
- The central O has one lone pair, leading to a bent molecular geometry.

Only NO₂⁺ satisfies the condition of having two bonding pairs and no lone pairs on the central atom, which VSEPR predicts to be linear. Therefore, the species with a linear shape is NO₂⁺.