A solid having density of `9 xx 10^(3) kg m^(-3)` forms face centred cubic crystals of edge length `200 sqrt2` pm. What is the molar mass of the solid ? [Avogadro constant `~= 6 xx 10^(23) mol^(-1), pi ~= 3`]

Options

A. 0.0305 kg m`ol^(-1)`
B. 0.0216 kg m`ol^(-1)`
C. 0.4320 kg m`ol^(-1)`
D. 0.0432 kg m`ol^(-1)`

Explanation

To solve the problem, we need to find the molar mass of a solid that forms face-centered cubic (FCC) crystals, given its density and edge length. Let's go through the steps systematically.

### Step 1: Identify the given values
- Density (ρ) = \( 9 \times 10^{3} \, \text{kg/m}^3 \)
- Edge length (a) = \( 200 \sqrt{2} \, \text{pm} \) = \( 200 \sqrt{2} \times 10^{-12} \, \text{m} \)
- Avogadro's number (N_A) = \( 6 \times 10^{23} \, \text{mol}^{-1} \)

### Step 2: Calculate the volume of the unit cell
...