The correct statement regarding `ClO_(n)^(-)` molecular ion is:

Options

A. On decreasing value of 'n', `Cl-O` bond order increases
B. On increasing value of 'n', Cl-O bond length increases
C. On increasing value of n, oxidation number of central atom increases
D. On increasing value of n, hybrid orbitals on central atom increases

Answer

To analyze the molecular ion ClO_n^(-) and determine the correct statement regarding it, we will follow these steps:

### Step 1: Understand the Molecular Ion ClO_n^(-)
The molecular ion ClO_n^(-) consists of chlorine (Cl) and oxygen (O) atoms. The subscript n indicates the number of oxygen atoms bonded to the chlorine atom, and the negative charge indicates that the overall charge of the ion is -1.

### Step 2: Determine the Structure for Different Values of n
1. **For n = 1 (ClO^(-))**:
- Chlorine has 7 valence electrons, and oxygen has 6 valence electrons.
- Total valence electrons = 7 + 6 + 1 (for the negative charge) = 14 electrons.
- The structure will have a single bond between Cl and O, with Cl having a formal charge of +1 and O having a formal charge of -1.

2. **For n = 2 (ClO2^(-))**:
- Total valence electrons = 7 + 2*6 + 1 = 20 electrons.
- The structure will have one double bond between Cl and one O, and a single bond with the other O. The formal charges will balance out to keep the overall charge -1.

3. **For n = 3 (ClO3^(-))**:
- Total valence electrons = 7 + 3*6 + 1 = 26 electrons.
- The structure will have one Cl atom bonded to three O atoms, with one of the O atoms having a double bond. The formal charges will also balance out to maintain the -1 charge.

### Step 3: Calculate Bond Order
The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} \]

1. **For ClO^(-)**:
- Bond order = 1 (single bond).

2. **For ClO2^(-)**:
- Bond order = 1.5 (one double bond and one single bond).

3. **For ClO3^(-)**:
- Bond order = 1.67 (more double bonds increase the bond order).

### Step 4: Analyze the Trends
- As n increases, the bond order increases.
- The oxidation state of Cl also increases with n (from +1 in ClO^(-) to +5 in ClO3^(-)).
- The hybridization remains the same (sp3) across these ions.

### Step 5: Evaluate the Statements
1. **On decreasing value of n, ClO bond order decreases**: True, as we observed that bond order increases with increasing n.
2. **On increasing value of n, ClO bond length increases**: False, bond length decreases with increasing bond order.
3. **On increasing value of n, oxidation number of central atom increases**: True, as the oxidation state increases from +1 to +5.
4. **Hybridization of central atom increases with n**: False, hybridization remains the same.

### Conclusion
The correct statement regarding ClO_n^(-) molecular ion is: **On increasing value of n, the oxidation number of the central atom increases.**