Calculate the approximate number of unit cells present in 1 g of gold. Given that gold cyrstallises in a face centred cubic lathce (Given atomic mass of gold = 197 u).

Explanation

To calculate the approximate number of unit cells present in 1 g of gold, we can follow these steps:

### Step 1: Calculate the number of moles of gold in 1 g
The atomic mass of gold (Au) is given as 197 u (unified mass).

Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{1 \text{ g}}{197 \text{ g/mol}} \approx 0.00508 \text{ moles} \]

### Step 2: Determine the number of atoms in the moles of gold
Using Avogadro's number (approximately \(6.022 \times 10^{23}\) atoms/mol), we can find the total number of atoms in the calculated moles:
\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of atoms} = 0.00508 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 3.06 \times 10^{21} \text{ atoms} \]

### Step 3: Determine the number of unit cells in gold
Gold crystallizes in a face-centered cubic (FCC) lattice structure, which contains 4 atoms per unit cell. Therefore, the number of unit cells can be calculated as:
\[ \text{Number of unit cells} = \frac{\text{Number of atoms}}{\text{Number of atoms per unit cell}} \]
\[ \text{Number of unit cells} = \frac{3.06 \times 10^{21} \text{ atoms}}{4} \approx 7.65 \times 10^{20} \text{ unit cells} \]

### Final Answer
The approximate number of unit cells present in 1 g of gold is \(7.65 \times 10^{20}\).

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