In which of the following compound Mn shoes minimum radius ?

Options

A. MnO2
B. KMnO4
C. MnO
D. None of these

Explanation

To determine in which compound manganese (Mn) shows the minimum radius, we need to analyze the oxidation states of Mn in the given compounds and understand how oxidation state affects ionic radius.

### Step-by-Step Solution:

1. **Identify the Compounds**: The compounds given are MnO2, KMnO4, and MnO.

2. **Determine the Oxidation States of Mn**:
- **For MnO2**:
- Let the oxidation state of Mn be \( x \).
- The oxidation state of oxygen is -2.
- The equation becomes:
\[ x + 2(-2) = 0 \implies x - 4 = 0 \implies x = +4 \]
- **For KMnO4**:
- Let the oxidation state of Mn be \( x \).
- The oxidation state of potassium (K) is +1 and the oxidation state of oxygen is -2.
- The equation becomes:
\[ 1 + x + 4(-2) = 0 \implies 1 + x - 8 = 0 \implies x - 7 = 0 \implies x = +7 \]
- **For MnO**:
- Let the oxidation state of Mn be \( x \).
- The oxidation state of oxygen is -2.
- The equation becomes:
\[ x + (-2) = 0 \implies x + 2 = 0 \implies x = +2 \]

3. **Compare the Oxidation States**:
- Mn in MnO2 has an oxidation state of +4.
- Mn in KMnO4 has an oxidation state of +7.
- Mn in MnO has an oxidation state of +2.

4. **Analyze the Effect of Oxidation State on Ionic Radius**:
- The higher the oxidation state of a metal ion, the smaller its ionic radius due to increased effective nuclear charge.
- Therefore, Mn in KMnO4 (+7) will have the smallest radius compared to Mn in MnO2 (+4) and MnO (+2).

5. **Conclusion**:
- Since Mn has the highest oxidation state (+7) in KMnO4, it will show the minimum radius in this compound.

### Final Answer:
Mn shows the minimum radius in the compound **KMnO4**.