Which of the following exists as covalent crystals in the solid state?

First, let us recall the basic idea of how substances can arrange themselves in the solid state. Broadly, we classify crystalline solids into four main types: (i) ionic crystals, (ii) molecular crystals, (iii) metallic crystals and (iv) covalent (also called network) crystals. A covalent or network crystal is one in which each atom is linked to its nearest neighbours by strong directional covalent bonds extending throughout the entire crystal lattice, producing one giant molecule. The classic textbook examples are $$\text{SiO}_2$$ (quartz), $$\text{SiC}$$ (silicon carbide) and elemental silicon (in its diamond‐type lattice).

Now we examine every substance given in the options one by one, asking ourselves: “Does this element form a giant three-dimensional covalent network in the solid, or does it exist as discrete molecules held together only by weak van der Waals forces?”

We start with sulphur. In its most common crystalline form ($$\alpha$$-sulphur or rhombic sulphur), each elementary unit is an $$S_8$$ crown-shaped molecule. These $$S_8$$ rings are neutral, completed valence shells, and the rings are packed in the lattice with only weak intermolecular London dispersion forces acting between them. There is no infinite covalent network extending throughout the solid, so sulphur is classified as a molecular crystal, not a covalent crystal.

Next is phosphorus. The common allotrope that is crystalline under ordinary conditions is red or violet phosphorus, in which $$P_4$$ tetrahedral molecules are linked into polymeric chains, but these chains are not fully three-dimensional networks; the bonding between chains remains relatively weak. White phosphorus is definitely molecular ($$P_4$$). Hence, elemental phosphorus does not form a fully extended covalent framework like diamond or silicon does. Therefore it is not a covalent network crystal in the strict sense used in solid-state chemistry.

We then consider iodine. At room temperature iodine exists as discrete $$I_2$$ molecules. These diatomic molecules are held together in the crystal lattice only by van der Waals forces (specifically, London dispersion forces enhanced by iodine’s large, easily polarisable electron cloud). Thus crystalline iodine is also a molecular solid, not a network covalent solid.

Finally we come to silicon. Elemental silicon adopts the same three-dimensional tetrahedral arrangement as diamond. Each silicon atom forms four strong $$sp^3$$ hybridised $$\sigma$$ covalent bonds to four neighbour silicon atoms, and this pattern repeats indefinitely in all directions. This means there are no discrete $$Si_2$$ or $$Si_4$$ molecules: the whole crystal is a single giant covalent network. Because every bond throughout the lattice is a strong covalent bond, silicon exhibits the physical properties characteristic of covalent crystals—very high melting point, great hardness, brittleness and semiconducting behaviour.

Piecing everything together, only silicon among the given choices satisfies the definition of a covalent (network) crystal.

Hence, the correct answer is Option D.