Question

Tungsten has the highest melting point of any metal in the periodic table: \(3422{ }^{\circ} \mathrm{C}\). The distance between \(\mathrm{W}\) atoms in tungsten metal is \(2.74 \AA\). (a) What is the atomic radius of a tungsten atom in this environment? (This radius is called the metallic radius.) (b) If you put tungsten metal under high pressure, predict what would happen to the distance between \(\mathrm{W}\) atoms.

Short answer

The atomic (metallic) radius of a tungsten atom is approximately \(1.37 \AA\). Under high pressure, the distance between tungsten atoms is expected to decrease as the atoms are forced to move closer together.

Step-by-step solution

Understanding the relationship between atomic radius and distance between atoms

In a metallic crystal, the distance between two adjacent atoms gives an approximate estimation of their combined atomic radii. As the atoms are closely packed, we can assume that the distance between the centers of two tungsten atoms is approximately equal to the sum of their atomic radii. So, we can represent that as follows: Distance between atoms = 2 * Atomic radius of tungsten

Calculate the atomic radius of tungsten

Given that the distance between tungsten atoms is 2.74 Å (Angstrom), we can use the above equation to calculate the atomic radius of tungsten: \(2 * Atomic\, radius\, of\, tungsten = 2.74 \AA\) Divide both sides by 2 to find the atomic radius of tungsten: \(Atomic\, radius\, of\, tungsten = 1.37 \AA\) So, the atomic (metallic) radius of a tungsten atom is approximately 1.37 Å.

Predict the effect of high pressure on the distance between tungsten atoms

Under high pressure, atoms are forced to move closer together. Since the metallic crystal is closely packed, we can predict that the distance between tungsten atoms will decrease under high pressure. The atomic radii themselves are not expected to change significantly, but the increased pressure will cause the atoms to be more tightly packed. In conclusion, the atomic radius of a tungsten atom in its metallic environment is approximately 1.37 Å, and the distance between tungsten atoms is expected to decrease under high pressure.

Key concepts

Atomic Radius

The atomic radius is a measure of the size of an atom from its nucleus to the outermost electron cloud. In metallic bonding, atoms are closely packed in a lattice structure. This tight arrangement allows us to approximate the distance between two adjacent metallic atoms as twice the atomic radius.
When calculating the atomic radius in a metal like tungsten, we take the measured interatomic distance and divide it by two. For tungsten, with a distance of 2.74 Å between atoms, the atomic radius is 1.37 Å.
The atomic radius can affect various physical properties of the material, such as electrical conductivity and hardness. Understanding this concept helps explain why some metals are more suitable than others for specific applications.

Melting Point

Melting point is the temperature at which a solid becomes a liquid. Tungsten, with a melting point of 3422 °C, has the highest melting point of any metal. This high melting point indicates strong bonds between tungsten atoms.
The strength and type of bonding in a metal, which is in part determined by its atomic structure and radius, impacts how much energy is needed to break these bonds. Metals with smaller atomic radii often have higher melting points because their atoms are packed more tightly together, increasing the number of bonds between them.
Tungsten's high melting point makes it an excellent choice for products that must endure high temperatures, such as light bulb filaments and heating elements in furnaces.

High Pressure Effects

When a material is subjected to high pressure, the atoms are forced closer together. In metals, this typically causes a decrease in the distance between atoms, known as lattice compression.
Applying high pressure to tungsten would similarly reduce the interatomic distance. While the atomic radii remain largely unchanged, the external pressure causes the entire metallic lattice to become tighter.
This compression can affect various properties, potentially increasing the material's hardness and altering its electrical conductivity. High-pressure environment studies are essential for understanding how metals will behave under extreme conditions, aiding industries that operate in such environments, like aerospace and deep-sea exploration.