Question

A compound has fcc structure. If density of unit cell is 3.4 g cm$^{-3$, what is the edge length of unit cell? (Molar mass = 98-99)}

• A. 7.783 \AA
• B. 5.783 \AA
• C. 8.780 \AA
• D. 6.083 \AA

Hint:

In unit cell calculations, always ensure you know the structure type (fcc, bcc, etc.) and use the correct number of atoms per unit cell (e.g., 4 for fcc).

Answer 1

The Correct Option is B

Step 1: Using the formula for edge length.
For a compound with an fcc (face-centered cubic) structure, the relationship between the density (\(d\)), molar mass (\(M\)), Avogadro’s number (\(N_A\)), and edge length (\(a\)) is given by the formula: \[ d = \frac{Z \times M}{N_A \times a^3} \] Where \(Z = 4\) for fcc structure. We can rearrange this to solve for \(a\), the edge length: \[ a = \left(\frac{Z \times M}{N_A \times d}\right)^{1/3} \] Where: - \(Z = 4\) (for fcc structure) - \(M = 99 \, \text{g/mol}\) - \(d = 3.4 \, \text{g/cm}^3\) - \(N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}\)
Step 2: Calculation.
Substitute the values into the equation: \[ a = \left(\frac{4 \times 99}{6.022 \times 10^{23} \times 3.4}\right)^{1/3} \] After performing the calculation, we find that \(a = 5.783 \, \text{\AA}\).

Step 3: Conclusion.
The correct answer is (B) 5.783 \AA, which corresponds to the calculated edge length.