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: Write the formula
For a cubic cell, density is \(\rho = \frac{Z M}{N_A V}\), where \(Z\) is atoms per cell, \(M\) is molar mass and \(V\) is cell volume.

Step 2: Find Z
An fcc cell has \(8 \times \frac18 + 6 \times \frac12 = 4\) atoms.

Step 3: Substitute
\[ \rho = \frac{4 \times 108}{6.022\times 10^{23} \times 6.84\times 10^{-23}} = \frac{432}{41.19} \]
\[ \rho = 10.49\ \text{g cm}^{-3} \]

Step 4: Check the options
If Z were 2 (bcc) we would get about 5.2, which is not an option. Hence the answer is 10.49.

Final Answer:
The density of silver is 10.49 g per cubic centimetre. \[ \boxed{\text{(B)}\ 10.49\ \text{g cm}^{-3}} \]