Question

When silver crystallizes, it forms face centered cubic cells, if the volume of unit cells \(6.84\times 10^{-23} \text{cm}^3\). Calculate the density of silver. (Molar mass of silver is 108 g/mol, \(N_A = 6.022\times 10^{23}\))

• A. \(12.49 \text{gm cm}^{-3}\)
• B. \(10.49 \text{gm cm}^{-3}\)
• C. \(16.89 \text{gm cm}^{-3}\)
• D. \(20.49 \text{gm cm}^{-3}\)

Hint:

Density equals Z times molar mass divided by Avogadro number times cell volume, with Z = 4 for fcc.

Answer 1

The Correct Option is B

Step 1: Mass and volume of one cell
Mass of one cell is $\frac{4 \times 108}{6.022\times 10^{23}} = 7.174\times 10^{-22}$ g.

Step 2: Divide
$\rho = \frac{7.174\times 10^{-22}}{6.84\times 10^{-23}} = 10.49\ \text{g cm}^{-3}$.

Step 3: Result
Option (B).

Final Answer:
10.49 g per cm3. \[ \boxed{\text{(B)}\ 10.49\ \text{g cm}^{-3}} \]