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

Options

A. `0.4 xx N_(A)`
B. `0.1 xx N_(A)`
C. `4 xx N_(A)`
D. `N_(A)//40`

Explanation

To calculate the number of unit cells in 8 g of element X with an atomic weight of 80 g/mol and an FCC structure, follow these steps:

### Step 1: Calculate the number of moles of element X in 8 g.
The number of moles (n) can be calculated using the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
Here, the mass of X is 8 g and the molar mass is 80 g/mol.

\[ n = \frac{8 \, \text{g}}{80 \, \text{g/mol}} = 0.1 \, \text{mol} \]

### Step 2: Calculate the number of atoms in 0.1 moles of element X.
Using Avogadro's number (NA), which is approximately \(6.022 \times 10^{23}\) atoms/mol, we can find the total number of atoms in 0.1 moles.

\[ \text{Number of atoms} = n \times N_A = 0.1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \]
\[ \text{Number of atoms} = 6.022 \times 10^{22} \, \text{atoms} \]

### Step 3: Determine the number of unit cells.
In an FCC structure, each unit cell contains 4 atoms. Therefore, the number of unit cells can be calculated by dividing the total number of atoms by the number of atoms per unit cell.

\[ \text{Number of unit cells} = \frac{\text{Number of atoms}}{\text{Number of atoms per unit cell}} = \frac{6.022 \times 10^{22} \, \text{atoms}}{4} \]
\[ \text{Number of unit cells} = 1.5055 \times 10^{22} \, \text{unit cells} \]

### Final Answer:
The number of unit cells in 8 g of element X is approximately \(1.5055 \times 10^{22}\) unit cells.

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