An element `X (At,wt = 80 g//mol)` having fcc structure, calculate the number of unit cells in `8g of X`

Options

A. `0.4xxN_(A)`
B. `0.1 xxN_(A)`
C. `4 xxN_(A)`
D. `N_A / 40`

Answer

To solve the problem of calculating the number of unit cells in 8 grams of element X with an atomic weight of 80 g/mol and an FCC structure, we can follow these steps:

### Step 1: Determine the number of moles in 8 grams of X
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Given that the mass is 8 g and the molar mass is 80 g/mol:
\[ \text{Number of moles} = \frac{8 \, \text{g}}{80 \, \text{g/mol}} = 0.1 \, \text{mol} \]

### Step 2: Calculate the number of atoms in 0.1 moles of X
Using Avogadro's number (\(N_A = 6.022 \times 10^{23}\) atoms/mol), we can find the total number of atoms:
\[ \text{Number of atoms} = \text{Number of moles} \times N_A = 0.1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{22} \, \text{atoms} \]

### Step 3: Determine the number of atoms per unit cell in FCC structure
In a face-centered cubic (FCC) structure, 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:
\[ \text{Number of unit cells} = \frac{\text{Total number of atoms}}{\text{Number of atoms per unit cell}} = \frac{6.022 \times 10^{22} \, \text{atoms}}{4 \, \text{atoms/unit cell}} = 1.5055 \times 10^{22} \, \text{unit cells} \]

### Final Answer
Thus, the number of unit cells in 8 grams of element X is approximately:
\[ 1.5055 \times 10^{22} \, \text{unit cells} \]

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