Sodium crystallizes in a face centred cubic lattice. The approximate number of unit cells in 5.0 g of sodium is (Atomic mass of sodium = 23 mu)

Options

A. `32.7 × 10_(22)`
B. 3.27 x 10_(22)
C. 6.54 × 10_(22)
D. `65.4 × 10_(22)`

Answer

To find the approximate number of unit cells in 5.0 g of sodium, which crystallizes in a face-centered cubic (FCC) lattice, we can follow these steps:

### Step 1: Calculate the number of moles of sodium
The number of moles can be calculated using the formula:

\[ \text{Number of moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g/mol)}} \]

Given:
- Mass of sodium = 5.0 g
- Molar mass of sodium = 23 g/mol

\[ \text{Number of moles} = \frac{5.0 \, \text{g}}{23 \, \text{g/mol}} \approx 0.217 \, \text{mol} \]

### Step 2: Calculate the number of atoms in sodium
Using Avogadro's number (\(N_A = 6.022 \times 10^{23} \, \text{atoms/mol}\)), we can find the total number of atoms:

\[ \text{Number of atoms} = \text{Number of moles} \times N_A \]

\[ \text{Number of atoms} = 0.217 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 1.306 \times 10^{23} \, \text{atoms} \]

### Step 3: Determine the number of unit cells
In a face-centered cubic (FCC) lattice, there are 4 atoms per unit cell. Therefore, the number of unit cells can be calculated as:

\[ \text{Number of unit cells} = \frac{\text{Number of atoms}}{4} \]

\[ \text{Number of unit cells} = \frac{1.306 \times 10^{23} \, \text{atoms}}{4} \approx 3.265 \times 10^{22} \, \text{unit cells} \]

### Final Answer
The approximate number of unit cells in 5.0 g of sodium is \(3.27 \times 10^{22}\).

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