To determine which set of atoms has the shortest bond length among [tex]\( N - N \)[/tex], [tex]\( N = N \)[/tex], and [tex]\( N \equiv N \)[/tex], we need to understand the relationship between bond length and bond order.
1. Bond Order and Bond Length:
- Bond order refers to the number of shared electron pairs between two atoms.
- A single bond ([tex]\( N - N \)[/tex]) has a bond order of 1.
- A double bond ([tex]\( N = N \)[/tex]) has a bond order of 2.
- A triple bond ([tex]\( N \equiv N \)[/tex]) has a bond order of 3.
2. Bond Length Characteristics:
- Single bonds are generally the longest because there is only one pair of electrons shared, resulting in less overlap and weaker attraction between the atoms.
- Double bonds are shorter than single bonds due to increased electron density and greater attraction between the atoms.
- Triple bonds are the shortest because they have the highest electron density, leading to the strongest attraction and closest bond distance.
Given these points, we conclude that the triple bond ([tex]\( N \equiv N \)[/tex]) has the shortest bond length.
Thus, the correct answer choice is:
C. [tex]\( N \equiv N \)[/tex]
