Question

Calculate the number of atoms present in 1.625 g metal if it forms bcc unit cell structure.
\([ρ\times a^3 = 3.25\times 10^{-22} \text{g}]\)

• A. \(2.0\times 10^{22}\)
• B. \(1.5\times 10^{22}\)
• C. \(2.5\times 10^{22}\)
• D. \(1.0\times 10^{22}\)

Hint:

Mass of one unit cell = rho x a^3, and a bcc cell holds 2 atoms.

Answer 1

The Correct Option is D

Step 1: Mass of one cell
Given $\rho a^3 = 3.25 \times 10^{-22}$ g, which is the mass of a single cell.

Step 2: Count cells
$1.625 / 3.25 \times 10^{-22} = 5 \times 10^{21}$ cells.

Step 3: Count atoms
bcc has $8 \times \frac{1}{8} + 1 = 2$ atoms per cell, so total $= 1.0 \times 10^{22}$. Option (D).

Final Answer:
Option (D). \[ \boxed{1.0 \times 10^{22}} \]