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 amu)

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, we can follow these steps:

### Step 1: Calculate the number of moles of sodium
To find the number of moles of sodium in 5.0 g, we use the formula:

\[ \text{Number of moles} = \frac{\text{Weight}}{\text{Molar mass}} \]

Given:
- Weight 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
Now, we can calculate the total number of atoms using Avogadro's number (\(N_A = 6.022 \times 10^{23} \, \text{atoms/mol}\)):

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

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

### Step 3: Determine the number of unit cells
In a face-centered cubic (FCC) lattice, there are 4 atoms per unit cell. Therefore, we can find the number of unit cells by dividing the total number of atoms by the number of atoms per unit cell:

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

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

### Step 4: Round the result
Rounding \(3.265 \times 10^{22}\) to two decimal places gives us approximately \(3.27 \times 10^{22}\) unit cells.

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

---