Exhibit 21-3
The following question(s) pertain to Iron which has a body-centered cubic unit cell. It has a molar mass of 55.847 g·mol^-¹and a density of 7.86 g·cm^-³.
Refer to Exhibit 21-3. What is the radius of a single iron atom?

Question

Quizplus · Accepted Answer

The radius of an atom in a body-centered cubic (BCC) unit cell can be calculated using the formula: $ r = \frac{\sqrt{3}a}{4} $. First, calculate the edge length $ a $ using the density formula: $ \text{density} = \frac{\text{mass}}{\text{volume}} $. The volume of the unit cell is $ a^3 $, and the mass of the unit cell is the molar mass divided by Avogadro's number, multiplied by the number of atoms per unit cell (2 for BCC). Solving for $ a $ and substituting into the radius formula gives approximately 1.24 Å.

Exhibit 21-3 The Following Question(s) Pertain to Iron Which Has a Body-Centered