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 can follow these steps:

### Step 1: Determine the formula mass of Na₂O
- The atomic mass of Sodium (Na) is approximately 23 g/mol.
- The atomic mass of Oxygen (O) is approximately 16 g/mol.
- Therefore, the formula mass of Na₂O = (2 × 23) + (1 × 16) = 46 + 16 = 62 g/mol.

**Hint:** Calculate the formula mass by adding the contributions of each element in the compound.

### Step 2: Analyze the arrangement of ions in the unit cell
- In Na₂O, Sodium ions (Na⁺) occupy the tetrahedral voids, while Oxide ions (O²⁻) are arranged in a face-centered cubic (FCC) structure.
- In an FCC arrangement, there are 8 corner atoms and 6 face-centered atoms.

**Hint:** Understand the arrangement of ions in the crystal structure to determine how many of each ion are present in the unit cell.

### Step 3: Calculate the number of Na⁺ ions in the unit cell
- There are 8 tetrahedral voids in the unit cell, each occupied by one Na⁺ ion.
- Therefore, there are 8 Na⁺ ions in the unit cell.

**Hint:** Remember that each tetrahedral void can hold one ion, and count the total number of voids available in the unit cell.

### Step 4: Calculate the number of O²⁻ ions in the unit cell
- For the O²⁻ ions in the FCC arrangement:
- Contribution from corners: 8 corners × (1/8) = 1 O²⁻ ion.
- Contribution from face centers: 6 faces × (1/2) = 3 O²⁻ ions.
- Total O²⁻ ions = 1 + 3 = 4 O²⁻ ions.

**Hint:** Use the contributions from corners and face centers to find the total number of ions in the unit cell.

### Step 5: Determine the total number of formula units in the unit cell
- Since there are 8 Na⁺ ions and 4 O²⁻ ions, we can form 4 Na₂O formula units in the unit cell (2 Na⁺ ions per Na₂O).

**Hint:** The number of formula units is determined by the ratio of cations to anions in the unit cell.

### Step 6: Calculate the mass of the unit cell
- The mass of the unit cell = Number of formula units × Formula mass of Na₂O.
- Therefore, mass of the unit cell = 4 × 62 g/mol = 248 g/mol.

**Hint:** Multiply the number of formula units by the formula mass to find the total mass of the unit cell.

### Conclusion
The mass of the unit cell of Na₂O is 4 times the formula mass of Na₂O.

**Final Answer:** The mass of the unit cell of Na₂O is 4 times the formula mass of Na₂O.