Tungsten crystallizes in body centred cubic lattice. Calculate the number of unit cells in 1.5 g of tungsten crystallizes in body centred cubic lattice . Calculate the number of unit cells in 1.5 g of tungsten (Atomic mass of tungsten = 184 u).

Explanation

To calculate the number of unit cells in 1.5 g of tungsten, which crystallizes in a body-centered cubic (BCC) lattice, we can follow these steps:

### Step 1: Determine the number of atoms per unit cell in BCC
In a body-centered cubic (BCC) lattice, there are:
- 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom to the unit cell.
- 1 atom in the center contributing 1 whole atom.

Thus, the total number of atoms per unit cell in BCC is:
\[ \text{Total atoms} = 8 \times \frac{1}{8} + 1 = 2 \text{ atoms} \]

### Step 2: Calculate the number of moles of tungsten in 1.5 g
The atomic mass of tungsten (W) is given as 184 g/mol. To find the number of moles in 1.5 g, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{1.5 \, \text{g}}{184 \, \text{g/mol}} \approx 0.00815 \, \text{mol} \]

### Step 3: Calculate the number of atoms in 1.5 g of tungsten
Using Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol), we can find the total number of atoms:
\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Number of atoms} = 0.00815 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 4.91 \times 10^{21} \, \text{atoms} \]

### Step 4: Calculate the number of unit cells
Since each unit cell contains 2 atoms, the number of unit cells can be calculated as:
\[ \text{Number of unit cells} = \frac{\text{Number of atoms}}{\text{Atoms per unit cell}} \]
Substituting the values:
\[ \text{Number of unit cells} = \frac{4.91 \times 10^{21} \, \text{atoms}}{2} \approx 2.45 \times 10^{21} \, \text{unit cells} \]

### Final Answer
The number of unit cells in 1.5 g of tungsten is approximately \(2.45 \times 10^{21}\).

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