Q.What is common between diamond and graphite?

Graphite is the thermodynamically most stable form of carbon under normal conditions.

Among carbon's allotropes/forms, graphite has the lowest standard Gibbs free energy (and lowest enthalpy) at room temperature and pressure, making it the thermodynamically most stable form — this is why diamond is described as being 'metastable' (kinetically stable but thermodynamically less stable than graphite, converting to graphite only under extreme conditions over very long timescales). Peat and coal are impure, amorphous, less-ordered carbonaceous materials, not thermodynamically stable reference forms of carbon.

Fullerene, graphite, and graphene share the same trigonal-planar, sp² carbon bonding of fused six-membered (and, in fullerene, also five-membered) rings; dry ice is solid $CO_2$, whose carbon is sp hybridised in a linear molecule, so it is the odd one out.

Graphite consists of 2-D sheets of sp² carbon atoms, each bonded to three neighbours in a hexagonal honeycomb lattice, with a delocalised pi-electron system above and below each sheet. Graphene is simply a single isolated layer of graphite — chemically identical sp² bonding. Fullerene ($C_{60}$ etc.) is a closed, curved cage built from the same three-sigma-bonds-per-carbon sp² framework, just curved by incorporating some five-membered rings among the hexagons. Dry ice, by contrast, is the solid form of carbon dioxide, $CO_2$, a small linear triatomic molecule ($O=C=O$) in which the central carbon forms two sigma bonds (to each oxygen) plus two pi bonds, giving it sp hybridisation (linear, 180° bond angle) — fundamentally different bonding from the extended sp² carbon networks of the other three.

Diamond is a giant covalent (network) solid, held together entirely by C–C covalent bonds.

In diamond, every carbon atom is sp³ hybridized and forms four strong covalent bonds to four neighbouring carbon atoms in a tetrahedral arrangement, extending throughout the crystal as a three-dimensional network. This is why diamond is extremely hard and has a very high melting point — properties characteristic of a covalent (network) solid, not an ionic or metallic one.

Each carbon in $C_{60}$ fullerene is bonded to exactly three other carbons (forming the closed, ball-shaped network of fused hexagons and pentagons), the same three-connected bonding pattern as planar graphite, so each carbon is $sp^2$ hybridised.

Fullerene $C_{60}$ consists of 60 carbon atoms arranged in a closed, roughly spherical (football/soccer-ball-shaped) cage made of 20 six-membered rings and 12 five-membered rings. Each carbon atom forms exactly three sigma bonds to three neighbouring carbon atoms (as in graphite's 2-D sheets), leaving one unhybridised p-orbital per carbon that contributes to a delocalised pi system over the cage surface. Three sigma bonds plus one delocalised p-orbital is the signature of $sp^2$ hybridisation (unlike diamond's four sigma bonds/$sp^3$ hybridisation).

Graphite's structure is stacked, planar sheets of hexagonally-arranged, sp2-hybridised carbon atoms.

In graphite, every carbon atom is sp2 hybridised and forms three strong sigma covalent bonds to three neighbouring carbon atoms (C-C bond length about 141.5 pm), building a continuous, flat, honeycomb-like network of fused hexagonal rings - essentially an infinite sheet, similar to a single layer of what is now called graphene. Each carbon atom's fourth (unhybridised) electron sits in a p-orbital perpendicular to the sheet; these p-orbitals overlap to give a delocalised pi-electron cloud spread over the whole sheet, which is why graphite conducts electricity along the plane of the layers.

Many such hexagonal sheets are then stacked one above another (interlayer spacing about 340 pm) and held together only by weak van der Waals forces, NOT covalent bonds. Because these forces are weak, the layers can easily slide over each other - this is why graphite is soft, slippery, and useful as a lubricant and in pencils, even though the covalent bonding within each sheet is very strong (giving graphite a high melting point).

(This is a text description of the layered hexagonal-sheet structure; no source figure was provided for this batch, so no diagram is reproduced here.)

Graphite is a giant covalent (network) solid — option (b).

From NCERT Class 11 Chemistry (p-Block, carbon allotropes): in graphite each carbon is sp² hybridised and covalently bonded to three neighbours, forming hexagonal sheets; the whole layer is one giant covalent network. The fourth electron is delocalised over the layer (giving electrical conductivity), but the structure itself is a covalent (network) solid, not molecular or metallic.

Graphite's electrons are delocalised/spread out across the layers — option (d).

From NCERT Class 11 Chemistry (p-Block, carbon allotropes): in graphite each carbon is sp² hybridised, forming three σ-bonds within a planar hexagonal sheet. The remaining unhybridised p-electron on every carbon forms a delocalised π-system spread over the entire layer. These mobile, delocalised electrons make graphite a good conductor of electricity and give its soft, slippery character.

Carbon exists in crystalline forms (diamond, graphite) and amorphous forms (lamp black, coke, charcoal) that lack a regular repeating lattice.

Carbon's allotropes are broadly divided into crystalline allotropes, where atoms are arranged in a well-defined repeating three-dimensional lattice (diamond: tetrahedral sp3 network; graphite: layered sp2 sheets), and amorphous allotropes, which consist of very fine crystallites of graphite arranged without long-range order. Lamp black (soot produced by incomplete combustion of oils/hydrocarbons) is a finely divided, structurally disordered form of carbon, so it is classified as amorphous rather than crystalline.

Graphite is the thermodynamically most stable allotrope of carbon at room temperature and pressure.

Carbon exists as diamond, graphite, fullerenes, etc. At ordinary temperature and pressure, graphite has the lowest free energy, so it is the reference (most stable) allotrope; diamond is only metastable and very slowly converts to graphite. That is why delta(f)H of graphite is taken as zero.