Question
Carbon is the only element that exists in three well-known allotropic forms. Compare the structure, bonding, and properties of diamond, graphite, and fullerene (C₆₀). Why does the same element behave so differently in each form?
Solution — Step by Step
Allotropes are different physical forms of the same element — same atoms, different arrangements. Carbon has 4 valence electrons, so it can hybridize as sp³, sp², or even sp, giving it unusual flexibility to form completely different structures.
In diamond, each carbon is sp³ hybridized and bonded to 4 other carbons in a tetrahedral arrangement. This forms a giant 3D covalent network where every bond is a strong σ-bond (C–C bond length = 154 pm).
Because all 4 valence electrons are used in bonding, there are no free electrons — diamond is a non-conductor. Every atom is locked in place, making diamond the hardest natural substance.
Each carbon in graphite is sp² hybridized, bonded to 3 others in a hexagonal (honeycomb) pattern. The remaining p orbital on each carbon overlaps sideways across the entire layer, forming a delocalized π-electron cloud.
This is the key: those delocalized electrons are free to move, so graphite conducts electricity. The layers are held together only by weak van der Waals forces — which is exactly why graphite is soft and slippery (used as a lubricant and in pencils).
Fullerene (Buckminsterfullerene) has 60 carbon atoms arranged in 20 hexagons and 12 pentagons — exactly like a football. The hybridization is close to sp², but slightly distorted because of the curved surface.
C₆₀ is a discrete molecule (not a network solid), making it soluble in organic solvents like toluene — unlike diamond or graphite.
| Property | Diamond | Graphite | Fullerene (C₆₀) |
|---|---|---|---|
| Hybridization | sp³ | sp² | ~sp² (distorted) |
| Structure | 3D network | Layered sheets | Closed cage |
| Hardness | Hardest known | Soft, slippery | Moderate |
| Electrical conductivity | Nil | Good (along layers) | Semiconducting |
| Appearance | Transparent | Black, lustrous | Dark solid |
| Solubility | Insoluble | Insoluble | Soluble in toluene |
The fundamental reason for all these differences: hybridization determines structure, and structure determines every property.
Why This Works
The sp³ hybridization in diamond uses all 4 electrons in σ-bonds. No lone electrons, no delocalization — this gives maximum bond strength in all 3 dimensions. A structure with no weak links is going to be extremely hard and thermally stable.
Graphite’s sp² hybridization leaves one electron per carbon in a p orbital perpendicular to the layer. When millions of these p orbitals line up, they form a continuous π-system — essentially a 2D metal. The layers have no covalent bond between them, just weak dispersion forces (~3.4 Å apart), so they slide over each other easily.
Fullerene is fascinating because introducing pentagons into an otherwise hexagonal sheet forces the flat layer to curve and close into a sphere. The slight strain from this curvature makes C₆₀ reactive enough to act as an electron acceptor — which is why it’s studied in solar cell research.
Alternative Method (For Exam Answers)
For boards, you can organize your answer around three parameters: structure → bonding → properties. Examiners want to see that chain of reasoning, not just a list of facts.
Write it as: “Because diamond has sp³ hybridization (structure), all electrons are in σ-bonds (bonding), therefore no free electrons and maximum hardness (properties).”
Repeat this logic for graphite and fullerene. You will score full marks for this approach in CBSE theory questions.
In JEE, fullerene questions often ask about the number of σ and π bonds in C₆₀. C₆₀ has 60 C–C single bonds in pentagons + 30 C=C double bonds in hexagons = 90 bonds total, with 60 σ-bonds from the framework and 30 additional π-bonds from the double bonds. Work this out from the structure rather than memorizing.
Common Mistake
Students often write “graphite conducts electricity because it has free electrons between layers.” This is partially wrong — the free electrons are within each layer (in the delocalized π-system), not floating between layers. Conductivity is highest along the layer plane, not perpendicular to it. In boards, writing “between layers” can cost you the explanation mark.
A second trap: calling fullerene an “infinite covalent network” like diamond. It is not — it is a discrete molecular solid with exactly 60 atoms. This distinction matters for why C₆₀ dissolves in organic solvents while diamond and graphite don’t.