Which of the following of manganese is amphoteric?

Options

A. `MnO_2`
B. `Mn_2O_3`
C. `Mn_2O_7`
D. `MnO`

Explanation

To determine which of the manganese oxides is amphoteric, we need to analyze the oxidation states of manganese in the given compounds and their corresponding acidic or basic nature.

### Step-by-Step Solution:

1. **Identify the Compounds**: The compounds we need to analyze are MnO2, Mn2O3, Mn2O7, and MnO.

2. **Calculate Oxidation States**:
- **For MnO2**:
- Oxygen (O) has an oxidation state of -2.
- For 2 O atoms: \( 2 \times (-2) = -4 \).
- Let the oxidation state of Mn be \( x \).
- The equation becomes: \( x + (-4) = 0 \) → \( x = +4 \).
- **For Mn2O3**:
- For 3 O atoms: \( 3 \times (-2) = -6 \).
- Let the oxidation state of Mn be \( x \) (for 2 Mn atoms: \( 2x \)).
- The equation becomes: \( 2x + (-6) = 0 \) → \( 2x = +6 \) → \( x = +3 \).
- **For Mn2O7**:
- For 7 O atoms: \( 7 \times (-2) = -14 \).
- The equation becomes: \( 2x + (-14) = 0 \) → \( 2x = +14 \) → \( x = +7 \).
- **For MnO**:
- For 1 O atom: \( -2 \).
- The equation becomes: \( x + (-2) = 0 \) → \( x = +2 \).

3. **Determine Acidic or Basic Nature**:
- Higher oxidation states tend to be acidic, while lower oxidation states tend to be basic.
- **MnO2** (Mn in +4 state): Can act as both acid and base (amphoteric).
- **Mn2O3** (Mn in +3 state): Generally basic.
- **Mn2O7** (Mn in +7 state): Acidic.
- **MnO** (Mn in +2 state): Basic.

4. **Conclusion**:
- Among the given manganese oxides, **MnO2** is amphoteric because it can exhibit both acidic and basic properties.

### Final Answer:
**MnO2 is the amphoteric oxide of manganese.**