Correct match is :-
`{:(,"Ion","Bond order of M-O bond",),((a),ClO_(4)^(-),(1)/(4),),((b),PO_(4)^(-3),(3)/(4),),((c),NO_(2)^(-),(2)/(3),),((d),CO_(3)^(-2),(5)/(3),):}`

Options

A. d
B. A,B,D
C. c,d
D. None

Answer

To solve the problem of matching the ions with their respective bond orders of the M-O bond, we will follow a systematic approach to calculate the bond order for each ion based on the oxidation state of the central atom and the number of oxygen atoms.

### Step-by-Step Solution:

1. **Identify the Ions and Their Oxidation States:**
- **(a) ClO₄⁻**:
- Let the oxidation state of Cl be x.
- The equation is: x + 4(-2) = -1 → x - 8 = -1 → x = +7.
- **(b) PO₄³⁻**:
- Let the oxidation state of P be y.
- The equation is: y + 4(-2) = -3 → y - 8 = -3 → y = +5.
- **(c) NO₂⁻**:
- Let the oxidation state of N be z.
- The equation is: z + 2(-2) = -1 → z - 4 = -1 → z = +3.
- **(d) CO₃²⁻**:
- Let the oxidation state of C be w.
- The equation is: w + 3(-2) = -2 → w - 6 = -2 → w = +4.

2. **Calculate the Bond Order for Each Ion:**
- The formula for bond order is given by:
\[ \text{Bond Order} = \frac{\text{Oxidation State of Central Atom}}{\text{Total Number of Oxygen Atoms}} \]

- **(a) ClO₄⁻**:
\[ \text{Bond Order} = \frac{+7}{4} = \frac{7}{4} \]

- **(b) PO₄³⁻**:
\[ \text{Bond Order} = \frac{+5}{4} = \frac{5}{4} \]

- **(c) NO₂⁻**:
\[ \text{Bond Order} = \frac{+3}{2} = \frac{3}{2} \]

- **(d) CO₃²⁻**:
\[ \text{Bond Order} = \frac{+4}{3} = \frac{4}{3} \]

3. **Match the Calculated Bond Orders with the Given Options:**
- **(a) ClO₄⁻**: Bond Order = \( \frac{7}{4} \) (not matching)
- **(b) PO₄³⁻**: Bond Order = \( \frac{5}{4} \) (not matching)
- **(c) NO₂⁻**: Bond Order = \( \frac{3}{2} \) (not matching)
- **(d) CO₃²⁻**: Bond Order = \( \frac{4}{3} \) (not matching)

4. **Conclusion:**
- None of the calculated bond orders match the options provided in the question. Therefore, the correct answer is **none of the above**.