Question

Which statement is consistent about diamond? (1) When an electrical potential is applied diamond becomes a valuable semiconductor (2) The hardest known substance with the highest melting point for an element. (3) A covalent network structure in which each \(\bar{C}\) atom uses sp \(^{3}\) hybrid orbitals. (4) A tetrahedral array of sigma bonds with bond lengths of \(154 \mathrm{pm}\). (a) 1,2 (b) \(1,2,3\) (c) \(2,3,4\) (d) 3,4

Short answer

(d) 3,4

Step-by-step solution

Analyze Option 1

The statement suggests that diamond becomes a valuable semiconductor when an electrical potential is applied. Diamond is known as an electrical insulator, not a semiconductor, under normal conditions. Therefore, statement (1) is incorrect.

Analyze Option 2

The statement claims that diamond is the hardest known substance with the highest melting point for an element. Diamond is indeed the hardest known natural material, but it does not have the highest melting point among elements. Therefore, statement (2) is only partly true as it is correct about the hardness but not about the melting point.

Analyze Option 3

This statement describes diamond as having a covalent network structure where each carbon atom utilizes sp³ hybrid orbitals. Diamond's crystal structure involves carbon atoms each forming four sp³ hybridized covalent bonds in a tetrahedral arrangement, so statement (3) is correct.

Analyze Option 4

The statement describes diamond as having a tetrahedral array of sigma bonds with bond lengths of 154 pm. Diamond's crystal structure features sigma bonds between carbon atoms with a tetrahedral arrangement, and the bond length is indeed approximately 154 pm, so statement (4) is correct.

Evaluate the Options

Review which options ( (a), (b), (c), (d) ) include the correct statement numbers as identified in the previous steps. Statements (3) and (4) have been identified as consistent with the properties of diamond. Therefore, the correct option is (d) 3,4.

Key concepts

Covalent Network Structure

Diamonds are a fascinating example of a covalent network structure, which contributes significantly to their renowned hardness and durability. In a covalent network, atoms are bonded together in an extensive three-dimensional lattice structure, rather than being discrete molecules. This interconnected grid of atoms leads to certain intricate properties.
In diamonds, each carbon atom forms a part of a giant covalent network. These atoms do not pair up into molecules; instead, they continuously extend their connections throughout the entire crystal. The robust network of bonds holding the carbon atoms together is what makes diamonds incredibly strong. Diamonds owe their superior hardness to the strength of these covalent bonds. While many other materials might have some covalent bonding, the structural order and arrangement in diamonds are uniquely rigorous.
The covalent network structure also implies that electrons are localized in specific areas, contributing to diamond's extreme electrical insulation properties. This tightly bound electron configuration means there are no free electrons to conduct electricity, contrasting with metals where electrons can move freely.

sp³ Hybridization

The concept of sp³ hybridization is crucial to understanding the molecular structure of diamonds. Hybridization is a model used to describe the atomic orbitals' mixing, allowing atoms to form bonds. For carbon atoms in diamonds, this hybridization results in the formation of four equivalent sp³ hybridized orbitals, optimized for bonding.
The sp³ hybridization involves the combination of one s atomic orbital and three p atomic orbitals from the carbon atom, creating four new equivalent orbitals positioned symmetrically in space. These hybrid orbitals point toward the corners of a tetrahedron, each forming strong sigma bonds with adjacent carbon atoms.
These sigma bonds result from the head-on overlap of the orbitals, creating maximum bond strength, which contributes to the diamond's structural rigidity. This symmetrical tetrahedral arrangement is one reason why diamonds have such exceptional physical properties, including exceptional hardness and thermal conductivity.

Tetrahedral Sigma Bonds

The structure of a diamond is defined by tetrahedral sigma bonds, a pivotal aspect of its remarkable characteristics. Sigma bonds are the strongest types of covalent bonds, formed by the linear, direct overlap of atomic orbitals.
In diamonds, each carbon atom forms four sigma bonds with its neighboring carbon atoms, resulting in a continuous lattice. The geometric arrangement of these bonds is tetrahedral, meaning they point towards the corners of a four-sided shape with equal angles between them. This results in bond lengths of approximately 154 pm, which is a standard measure within the diamond crystal's uniform lattice.
This unique bond configuration not only accounts for the diamond's strength but also its light-dispersing brilliance, as the bonds and electrons' arrangements do not allow for easy light penetration. The tetrahedral bond setup, being spread throughout each diamond, is a major factor in all diamonds having such high refractive indexes, contributing to their sparkling appearance.