Problem 21 - Chemistry: The Central Science

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.

Step-by-Step Solution

Answer

(a) The atomic radius (metallic radius) of a tungsten atom in this environment is approximately \(1.00 \, Å\). (b) Under high pressure, the distance between tungsten atoms would decrease, making the atoms move closer together.

Step 1: Understand the problem and given information

We are given the distance between atoms in tungsten (W), and we need to find the atomic radius. Tungsten has a Body Centered Cubic (BCC) crystal structure. In this structure, the atoms are at the corner of a cube lattice, and one atom is in the center. The distance between the atoms in this lattice is given as 2.74 Å. We need to determine the atomic radius (metallic radius) of a W atom under this environment.

Step 2: Body Centered Cubic (BCC) lattice

For a BCC crystal structure, the relationship between the distance between atoms (d) and the atomic radius (r) is given as: \(d = \sqrt{3} \cdot 2r\) We are given the atom's distance, and we need to find the atomic radius (r).

Step 3: Calculate the atomic radius

We are given the distance between atoms (d) as 2.74 Å. We can plug it into the equation to find the atomic radius (r): \(2.74 = \sqrt{3} \cdot 2r\) Now, we can solve for r: \(r = \frac{2.74}{\sqrt{3} \cdot 2}\) \(r ≈ 1.00 \, Å\) So the atomic radius of a tungsten atom in this environment (metallic radius) is approximately 1.00 Å.

Step 4: Predict the effect of high pressure on the distance between atoms

When a metal is put under high pressure, the atoms are compressed, and the atomic radius should decrease. As a result, the distance between atoms would also decrease. This means that, under high pressure, the W atoms in tungsten metal would move closer together.