Analysis show that nickel oxide consists of nickel ion with `96%` ions having `d^(8)` configuration and `4%` having `d^(7)` configuration. Which amongst the following best represents the formula of the oxide?

Options

A. `Ni_(1.02)O_(1.00)`
B. `Ni_(0.96)O_(1.00)`
C. `Ni_(0.98)O_(0.98)`
D. `Ni_(0.98)O_(1.00)`

Explanation

To determine the best formula for nickel oxide based on the given information, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Oxidation States of Nickel:**
- Nickel can exist in two oxidation states in this scenario: Ni²⁺ (which has a d⁸ configuration) and Ni³⁺ (which has a d⁷ configuration).
- According to the problem, 96% of the nickel ions are in the Ni²⁺ state, and 4% are in the Ni³⁺ state.

2. **Define the Proportions of Nickel Ions:**
- Let the total number of nickel ions in the oxide be represented as \( x \).
- The number of Ni²⁺ ions can be calculated as \( 0.96x \) and the number of Ni³⁺ ions as \( 0.04x \).

3. **Calculate the Total Positive Charge:**
- The total positive charge contributed by Ni²⁺ ions is \( 0.96x \times 2 = 1.92x \).
- The total positive charge contributed by Ni³⁺ ions is \( 0.04x \times 3 = 0.12x \).
- Therefore, the total positive charge from all nickel ions is:
\[ \text{Total Positive Charge} = 1.92x + 0.12x = 2.04x \]

4. **Determine the Negative Charge from Oxygen:**
- Each oxygen ion (O²⁻) contributes a charge of -2.
- Since there is one oxygen ion in the formula, the total negative charge is:
\[ \text{Total Negative Charge} = -2 \]

5. **Apply the Principle of Electrical Neutrality:**
- According to the principle of electrical neutrality, the total positive charge must equal the total negative charge:
\[ 2.04x = 2 \]

6. **Solve for \( x \):**
- Rearranging the equation gives:
\[ x = \frac{2}{2.04} \approx 0.9804 \]

7. **Write the Formula for Nickel Oxide:**
- Since \( x \) represents the number of nickel ions for one oxygen, the formula for nickel oxide can be approximated as:
\[ \text{Ni}_{0.98}\text{O} \]

8. **Conclusion:**
- The best representation of the formula of the oxide, based on the calculations, is \( \text{Ni}_{0.98}\text{O} \).