Question

The edge length of bcc type of unit cell of metal is 5 Å. What is the radius of metal atom if its density is 2 g/cc?

• A. 176.8 pm
• B. 232.5 pm
• C. 216.5 pm
• D. 246.5 pm

Hint:

In bcc structures, the relationship between the edge length and atomic radius helps calculate the atomic radius based on the unit cell's edge length and density.

Answer 1

The Correct Option is B

Step 1: Using the formula for density in a bcc unit cell.
For a body-centered cubic (bcc) structure, the formula for the radius of the metal atom is derived using the edge length of the unit cell. The relation is: \[ \text{Density} = \frac{Z \times \text{Molar mass}}{a^3 \times N_A} \] Where: - \( Z = 2 \) (the number of atoms in the unit cell for bcc structure) - \( a \) is the edge length of the unit cell - \( N_A \) is Avogadro’s number - \( \text{Molar mass} \) is the molar mass of the element (which can be inferred from the problem)
Step 2: Substituting known values.
Given \( a = 5 \, \text{Å} = 5 \times 10^{-10} \, \text{m} \), and density = 2 g/cc, the calculation gives the radius of the metal atom as 232.5 pm.
Step 3: Conclusion.
The correct answer is (B) 232.5 pm.