The C–C bond length refers to the distance between two bonded carbon atoms. Different allotropes of carbon have different bond lengths due to variations in their atomic arrangement and bonding character (single, double, or intermediate bonds).

Let's analyze the given options:

Diamond: In diamond, each carbon atom is $s{p}^3$ hybridized and forms four strong, pure single covalent bonds (C–C) in a tetrahedral network. The typical C–C single bond length is approximately $1.54 \mathrm{\AA }$.

Graphite: In graphite, each carbon atom is $s{p}^2$ hybridized. Within a layer, carbon atoms are connected by bonds that have a partial double bond character due to resonance. This results in a shorter bond length of approximately $1.42 \mathrm{\AA }$.

C₆₀ (Buckminsterfullerene) and C₇₀: These are closed cage molecules. In C₆₀, the carbon atoms are also $s{p}^2$ hybridized. The structure consists of 12 pentagons and 20 hexagons. The bonds at the junctions of two hexagons are shorter (double bond character, ~$1.38 \mathrm{\AA }$), and the bonds at the junctions of a pentagon and a hexagon are longer (single bond character, ~$1.45 \mathrm{\AA }$). The average C–C bond length in C₆₀ is about $1.44 \mathrm{\AA }$. C₇₀ has a similar elongated structure with comparable bond lengths.

Comparison:

• Diamond: Pure single bonds ($1.54 \mathrm{\AA }$)
• Graphite: Resonance-stabilized bonds with double bond character ($1.42 \mathrm{\AA }$)
• Fullerenes (C₆₀, C₇₀): Mix of bond types, average length (~$1.44 \mathrm{\AA }$)

Therefore, the maximum C–C bond length is found in diamond due to its pure single covalent bonds.

Related Topics & Formulae

Hybridization and Bond Length: The type of hybridization ($s{p}^3$, $s{p}^2$, $sp$) directly influences bond length. $s{p}^3$ bonds (single) are longest, while $sp$ bonds (triple) are shortest.

Bond Order: Bond length is inversely proportional to bond order. Higher bond order (double, triple) means shorter, stronger bonds. Single bonds have the lowest bond order (1) and are the longest.

Resonance: In molecules like graphite and benzene, resonance delocalizes electrons, giving bonds a fractional bond order between single and double, which shortens them compared to pure single bonds.