In which of the following compounds, maganese shows maximum radius?

Options

A. `MnO_(2)`
B. `KMnO_(4)`
C. `MnO`
D. `K_(3)[Mn(CN)_(6)]`

Explanation

To determine in which of the given compounds manganese shows the maximum radius, we need to analyze the oxidation states of manganese in each compound and understand how these oxidation states affect the ionic radius.

### Step-by-Step Solution:

1. **Identify the Compounds**: We need to analyze the following compounds:
- MnO2
- KMnO4
- MnO
- K3[Mn(CN)6]

2. **Determine the Oxidation State of Manganese in Each Compound**:
- **For MnO2**:
- Oxygen has an oxidation state of -2.
- Let the oxidation state of manganese be \( x \).
- The equation is: \( x + 2(-2) = 0 \) → \( x - 4 = 0 \) → \( x = +4 \).
- **For KMnO4**:
- Potassium has an oxidation state of +1, and oxygen has -2.
- Let the oxidation state of manganese be \( x \).
- The equation is: \( +1 + x + 4(-2) = 0 \) → \( x - 7 = 0 \) → \( x = +7 \).
- **For MnO**:
- Oxygen has an oxidation state of -2.
- Let the oxidation state of manganese be \( x \).
- The equation is: \( x + (-2) = 0 \) → \( x + 2 = 0 \) → \( x = +2 \).
- **For K3[Mn(CN)6]**:
- Potassium has an oxidation state of +1, and cyanide (CN) has -1.
- Let the oxidation state of manganese be \( x \).
- The equation is: \( 3(+1) + x + 6(-1) = 0 \) → \( x - 3 = 0 \) → \( x = +3 \).

3. **Summarize the Oxidation States**:
- MnO2: Mn is +4
- KMnO4: Mn is +7
- MnO: Mn is +2
- K3[Mn(CN)6]: Mn is +3

4. **Analyze the Ionic Radius**:
- The ionic radius decreases with increasing oxidation state due to the increased effective nuclear charge (Z effective) that pulls the electrons closer to the nucleus.
- Therefore, the order of ionic radius for manganese in these oxidation states is:
- Mn²⁺ (largest radius)
- Mn³⁺
- Mn⁴⁺
- Mn⁷⁺ (smallest radius)

5. **Conclusion**:
- Since Mn²⁺ has the largest radius, the compound where manganese shows the maximum radius is **MnO**.

### Final Answer:
Manganese shows the maximum radius in **MnO**.