Question

What is the \(\mathrm{C}-\mathrm{C}\) bond length (in angstroms) in diamond? (a) \(5.2\) (b) \(2.0\) (c) \(1.54\) (d) \(3.35\)

Short answer

Option (c) 1.54 angstroms.

Step-by-step solution

Understand the Problem

The exercise asks for the carbon-carbon bond length in diamond. This is a well-known fixed value in crystallography.

Identify Given Options

The options provided are: (a) 5.2, (b) 2.0, (c) 1.54, and (d) 3.35 angstroms.

Recall Average Bond Length in Diamond

From chemistry and materials science, the -C" bond length in diamond is known to be approximately 1.54 angstroms due to its tetrahedral bonding structure.

Match the Known Value with Options

Compare the known bond length of 1.54 angstroms with the given options. Option (c) matches the known -C" bond length in diamond.

Verify and Confirm

By confirming with standard reference sources in chemistry, option (c) 1.54 is indeed the correct bond length in diamond, corresponding to the densely packed covalent bonding structure.

Key concepts

Crystallography

Crystallography is the study of crystals and their structure. Crystals are made up of atoms, molecules, or ions that are systematically arranged in a repeating pattern. This creates a regular three-dimensional structure that extends in all directions. In the case of diamond, a well-known crystal, each carbon atom is lattice-bound to four other carbon atoms. This regular arrangement in diamond is a result of its strong covalent bonds, which are key to its hardness and high melting point.

Using techniques like X-ray crystallography, scientists can determine the precise arrangement of atoms in a crystal. This involves measuring how X-rays diffract when they pass through a crystal. The patterns created help researchers infer distances between atoms, leading to the identification of bond lengths, such as the 1.54 Å carbon-carbon bond length in diamond.

Tetrahedral Bonding Structure

The tetrahedral bonding structure is a key aspect of how carbon atoms connect in a diamond. A tetrahedron is a shape with four triangular faces, akin to a pyramid without a base.

In diamond, each carbon atom forms covalent bonds with four neighboring carbon atoms. This requires the carbon atom to create bonds at angles of approximately 109.5 degrees, which maximizes the distance between the bonds—explaining the arrangement seen in the tetrahedral structure. This configuration minimizes repulsions between electron pairs, creating a balanced and stable structure.

It's this efficient tetrahedral bonding that gives diamond its exceptional properties, such as extreme hardness and thermal conductivity, setting it apart from other carbon-based materials.

Covalent Bonding in Diamond

Covalent bonding in diamond involves the sharing of electron pairs between carbon atoms. This type of bond is very strong because the electrons are shared equally, allowing for high stability. In the case of diamond, the structure involves each carbon atom forming four covalent bonds with neighboring carbon atoms.

This creates a very rigid lattice structure where the atoms are closely packed. The strength of these covalent bonds is part of what makes diamond the hardest known natural material.

The repeating nature of these covalent bonds throughout the lattice is what results in the uniform bond length of 1.54 Å. These characteristics, alongside the tetrahedral arrangement, endow diamond with its remarkable set of physical properties, famously making it a highly valued gemstone and a tool material in industrial applications.