To determine which set of atoms has the shortest bond length, we need to understand the nature of the bonds between the nitrogen atoms:
1. Single Bond ([tex]$N - N$[/tex]):
- In a single bond, two nitrogen atoms share one pair of electrons.
- This results in a longer bond length as the bond is relatively weak compared to double and triple bonds.
2. Double Bond ([tex]$N = N$[/tex]):
- In a double bond, two nitrogen atoms share two pairs of electrons.
- This results in a shorter bond length compared to a single bond because the bond is stronger.
3. Triple Bond ([tex]$N \equiv N$[/tex]):
- In a triple bond, two nitrogen atoms share three pairs of electrons.
- This results in the strongest and therefore, the shortest bond length among the three options due to the increased number of shared electrons which pulls the atoms closer together.
Now, compare these bond lengths:
- Single bond ([tex]$N - N$[/tex]) has the longest bond length.
- Double bond ([tex]$N = N$[/tex]) has a shorter bond length than a single bond.
- Triple bond ([tex]$N \equiv N$[/tex]) has the shortest bond length.
Given this understanding, the shortest bond length is for the triple bond between the nitrogen atoms, represented as [tex]$N \equiv N$[/tex].
Thus, the correct answer choice is:
C.
