The mass of unit cell of `Na_(2)O` is

Options

A. Twice the formula mass of `Na_(2)O`
B. Four times the formula mass of `Na_(2)O`
C. Six times the formula mass of `Na_(2)O`
D. Thrice the formula mass of `Na_(2)O`

Answer

To find the mass of the unit cell of Na₂O, we will follow these steps:

### Step 1: Determine the composition of Na₂O
Na₂O consists of sodium (Na) and oxide (O) ions. In one formula unit of Na₂O, there are 2 sodium ions and 1 oxide ion.

### Step 2: Calculate the molar mass of Na₂O
- The molar mass of sodium (Na) = 23 g/mol
- The molar mass of oxygen (O) = 16 g/mol

Now, we can calculate the molar mass of Na₂O:
\[ \text{Molar mass of Na}_2\text{O} = (2 \times 23) + (1 \times 16) = 46 + 16 = 62 \text{ g/mol} \]

### Step 3: Determine the number of formula units in the unit cell
In the face-centered cubic (FCC) structure, the number of formula units (Z) in the unit cell is 4. This is because:
- There are 8 corner atoms, each contributing 1/8 of an atom to the unit cell.
- There are 6 face-centered atoms, each contributing 1/2 of an atom to the unit cell.
Thus, the total contribution is:
\[ Z = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 1 + 3 = 4 \]

### Step 4: Calculate the mass of the unit cell
Since there are 4 formula units of Na₂O in the unit cell, we can calculate the mass of the unit cell:
\[ \text{Mass of unit cell} = Z \times \text{Molar mass of Na}_2\text{O} \]
\[ \text{Mass of unit cell} = 4 \times \frac{62 \text{ g/mol}}{6.022 \times 10^{23} \text{ mol}^{-1}} \approx 4.12 \times 10^{-22} \text{ g} \]

### Final Answer
The mass of the unit cell of Na₂O is approximately \(4.12 \times 10^{-22} \text{ g}\).

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