1. We need to identify the nitrogen oxide in which nitrogen has an odd electron, i.e. a molecule with an unpaired electron on nitrogen.

2. Let us examine each oxide:

   (A) $N_2O$

   • Total valence electrons: $2(5) + 6 = 16$
   • This is an even-electron molecule.
   • It does not contain an odd electron on nitrogen.
   • So, A is incorrect.

   (B) $NO_2$

   • Total valence electrons: $5 + 2(6) = 17$
   • Since the total number of valence electrons is odd, $NO_2$ is an odd-electron molecule.
   • Its structure contains one unpaired electron, associated mainly with nitrogen.
   • So, B is correct.

   (C) $N_2O_3$

   • Total valence electrons: $2(5) + 3(6) = 28$
   • Even number of electrons, so no odd electron.
   • C is incorrect.

   (D) $N_2O_5$

   • Total valence electrons: $2(5) + 5(6) = 40$
   • Even-electron molecule.
   • D is incorrect.

3. Therefore, the oxide containing an odd electron at nitrogen is:

$\boxed{NO_2}$

4. Comparing with the stored correct answer:

• Stored correct answer: B
• Derived answer: B
• They match.