Sodium crystallises in body centred cubic unit cell. What is the approximate number of unit cells in 4.6 g of sodium ? Given that the atomic mass of sodium is 23 g `mol^(-1)`.

Explanation

To find the approximate number of unit cells in 4.6 g of sodium, we can follow these steps:

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

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

Given:
- Mass of sodium = 4.6 g
- Molar mass of sodium = 23 g/mol

Substituting the values:

\[ \text{Number of moles} = \frac{4.6 \, \text{g}}{23 \, \text{g/mol}} = 0.2 \, \text{moles} \]

### Step 2: Determine the number of atoms in the given moles of sodium.
To find the total number of atoms, we use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mol.

\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]

Substituting the values:

\[ \text{Number of atoms} = 0.2 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 1.2044 \times 10^{23} \, \text{atoms} \]

### Step 3: Determine the number of unit cells.
In a body-centered cubic (BCC) unit cell, there are 2 atoms per unit cell.

To find the number of unit cells, we can use the formula:

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

Substituting the values:

\[ \text{Number of unit cells} = \frac{1.2044 \times 10^{23} \, \text{atoms}}{2} = 6.022 \times 10^{22} \, \text{unit cells} \]

### Final Answer:
The approximate number of unit cells in 4.6 g of sodium is \(6.022 \times 10^{22}\).

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