In which of the following ionization processes, the bond order has increased and the magnetic behaviour has changed?

• Option A: $$\text{C}_2 \rightarrow \text{C}_2^+$$

  • $$\text{C}_2$$ ($$12\text{ electrons}$$): Bond order is $$2$$. All electrons are paired, making it diamagnetic.
  • $$\text{C}_2^+$$ ($$11\text{ electrons}$$): An electron is removed from a bonding molecular orbital ($$\pi_{2p}$$). The bond order decreases to $$1.5$$, and it becomes paramagnetic.
  • Result: Bond order decreased (Incorrect).



• Option B: $$\text{NO} \rightarrow \text{NO}^+$$

  • $$\text{NO}$$ ($$15\text{ electrons}$$): The last electron resides in an anti-bonding molecular orbital ($$\pi^*_{2p}$$). Bond order is $$2.5$$. It has one unpaired electron, making it paramagnetic.
  • $$\text{NO}^+$$ ($$14\text{ electrons}$$): Ionization removes this single unpaired electron from the anti-bonding orbital. The bond order increases to $$3$$, and because all remaining electrons are paired, its behavior shifts to diamagnetic.
  • Result: Bond order increased ($$2.5 \rightarrow 3$$) and magnetic behavior changed (paramagnetic $$\rightarrow$$ diamagnetic).



• Option C: $$\text{O}_2 \rightarrow \text{O}_2^+$$

  • $$\text{O}_2$$ ($$16\text{ electrons}$$): Bond order is $$2$$. It contains two unpaired electrons in anti-bonding orbitals, making it paramagnetic.
  • $$\text{O}_2^+$$ ($$15\text{ electrons}$$): An electron is removed from an anti-bonding orbital ($$\pi^*_{2p}$$). The bond order increases to $$2.5$$, but it still retains one unpaired electron, remaining paramagnetic.
  • Result: Magnetic behavior did not change (Incorrect).



• Option B: $$\text{N}_2 \rightarrow \text{N}_2^+$$

  • $$\text{N}_2$$ ($$14\text{ electrons}$$): Bond order is $$3$$ and it is diamagnetic.
  • $$\text{N}_2^+$$ ($$13\text{ electrons}$$): An electron is removed from a bonding orbital ($$\sigma_{2p_z}$$). The bond order decreases to $$2.5$$ and it becomes paramagnetic.
  • Result: Bond order decreased (Incorrect).

Conclusion:

Only the ionization of nitric oxide ($$\text{NO}$$) to the nitrosonium ion ($$\text{NO}^+$$) results in both an increased bond order and a shift in magnetic properties.

Answer: Option B — $$\text{NO} \rightarrow \text{NO}^+$$