Question

Copper crystallises in fcc unit cell with cell edge length of 3.608 x 10^-8 cm. The density of copper is 8.92 g cm^-3. Calculate the atomic mass of copper

• A. 63.1 u
• B. 31.55 u
• C. 60 u
• D. 65 u

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The density of a crystalline solid can be calculated using the parameters of its unit cell.
Key Formula or Approach:
\[ \rho = \frac{Z \times M}{a^{3} \times N_{A}} \]
Where:
\(\rho\) = density
\(Z\) = number of atoms per unit cell
\(M\) = atomic mass
\(a\) = cell edge length
\(N_{A}\) = Avogadro's number (\(6.022 \times 10^{23} \text{ mol}^{-1}\))
Step 2: Detailed Explanation:
Given:
Type of unit cell = fcc (\(Z = 4\))
\(a = 3.608 \times 10^{-8}\) cm
\(\rho = 8.92\) g \(cm^{-3}\)
Find \(M\).
\[ M = \frac{\rho \times a^{3} \times N_{A}}{Z} \]
\[ M = \frac{8.92 \times (3.608 \times 10^{-8})^{3} \times 6.022 \times 10^{23}}{4} \]
\[ M = \frac{8.92 \times 46.97 \times 10^{-24} \times 6.022 \times 10^{23}}{4} \]
\[ M = \frac{8.92 \times 46.97 \times 6.022 \times 10^{-1}}{4} \]
\[ M \approx \frac{2523 \times 10^{-1}}{4} \approx \frac{252.3}{4} = 63.075 \text{ u} \]
Step 3: Final Answer:
The atomic mass of copper is approximately 63.1 u. Option (1) is correct.