Copper crystallizes in a face centred cubic lattice. Calculate the number of unit cells in 1.2g of copper. Atomic mass of copper = 63.54.

Explanation

To solve the problem of calculating the number of unit cells in 1.2 g of copper, which crystallizes in a face-centered cubic (FCC) lattice, we can follow these steps:

### Step 1: Calculate the number of moles of copper
To find the number of moles of copper, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Given:
- Mass of copper = 1.2 g
- Atomic mass of copper = 63.54 g/mol

Calculating the number of moles:
\[ \text{Number of moles} = \frac{1.2 \, \text{g}}{63.54 \, \text{g/mol}} \approx 0.0189 \, \text{mol} \]

### Step 2: Calculate the number of atoms in copper
Using Avogadro's number, which is approximately \(6.022 \times 10^{23} \, \text{atoms/mol}\), we can find the total number of atoms in the given mass of copper:
\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of atoms} = 0.0189 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 1.14 \times 10^{22} \, \text{atoms} \]

### Step 3: Determine the number of atoms per unit cell in FCC
In a face-centered cubic (FCC) lattice, there are 4 atoms per unit cell.

### Step 4: Calculate the number of unit cells
To find the number of unit cells, we divide the total number of atoms by the number of atoms per unit cell:
\[ \text{Number of unit cells} = \frac{\text{Number of atoms}}{\text{Number of atoms per unit cell}} \]
\[ \text{Number of unit cells} = \frac{1.14 \times 10^{22} \, \text{atoms}}{4} \approx 2.85 \times 10^{21} \, \text{unit cells} \]

### Final Answer
The number of unit cells in 1.2 g of copper is approximately \(2.85 \times 10^{21}\).

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