`MnO_(4)^(-)` is a good oxidising agent in different mediums changing to
`MnO_(4)^(-)toMn^(2+)`
`toMnO_(4)^(2-)`
`toMnO_(2)`
`toMn_(2)O_(3)`
Changes in oxidation number respectively are

Options

A. 1,3,4,5
B. 5,4,3,2
C. 5,1,3,4
D. 2,6,4,3

Answer

To determine the changes in oxidation numbers for the conversions of \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \), \( \text{MnO}_4^{2-} \), \( \text{MnO}_2 \), and \( \text{Mn}_2\text{O}_3 \), we will follow these steps:

### Step 1: Determine the oxidation state of manganese in \( \text{MnO}_4^{-} \)

Let the oxidation state of manganese be \( x \).

Using the formula for oxidation states:
\[ x + 4(-2) = -1 \]
\[ x - 8 = -1 \]
\[ x = +7 \]

### Step 2: Calculate the change in oxidation state from \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \)

The oxidation state of manganese in \( \text{Mn}^{2+} \) is \( +2 \).

Change in oxidation state:
\[ +7 \text{ to } +2 \quad \Rightarrow \quad 7 - 2 = 5 \]

### Step 3: Determine the oxidation state of manganese in \( \text{MnO}_4^{2-} \)

Let the oxidation state of manganese be \( x \).

Using the formula for oxidation states:
\[ x + 4(-2) = -2 \]
\[ x - 8 = -2 \]
\[ x = +6 \]

### Step 4: Calculate the change in oxidation state from \( \text{MnO}_4^{2-} \) to \( \text{Mn}^{2+} \)

Change in oxidation state:
\[ +6 \text{ to } +2 \quad \Rightarrow \quad 6 - 2 = 4 \]

### Step 5: Determine the oxidation state of manganese in \( \text{MnO}_2 \)

Let the oxidation state of manganese be \( x \).

Using the formula for oxidation states:
\[ x + 2(-2) = 0 \]
\[ x - 4 = 0 \]
\[ x = +4 \]

### Step 6: Calculate the change in oxidation state from \( \text{MnO}_2 \) to \( \text{Mn}^{2+} \)

Change in oxidation state:
\[ +4 \text{ to } +2 \quad \Rightarrow \quad 4 - 2 = 2 \]

### Step 7: Determine the oxidation state of manganese in \( \text{Mn}_2\text{O}_3 \)

Let the oxidation state of manganese be \( x \).

Using the formula for oxidation states:
\[ 2x + 3(-2) = 0 \]
\[ 2x - 6 = 0 \]
\[ 2x = 6 \quad \Rightarrow \quad x = +3 \]

### Step 8: Calculate the change in oxidation state from \( \text{Mn}_2\text{O}_3 \) to \( \text{Mn}^{2+} \)

Change in oxidation state:
\[ +3 \text{ to } +2 \quad \Rightarrow \quad 3 - 2 = 1 \]

### Summary of Changes in Oxidation Number

1. From \( \text{MnO}_4^{-} \) to \( \text{Mn}^{2+} \): Change = 5
2. From \( \text{MnO}_4^{2-} \) to \( \text{Mn}^{2+} \): Change = 4
3. From \( \text{MnO}_2 \) to \( \text{Mn}^{2+} \): Change = 2
4. From \( \text{Mn}_2\text{O}_3 \) to \( \text{Mn}^{2+} \): Change = 1

Thus, the changes in oxidation numbers respectively are: **5, 4, 2, 1**.

### Final Answer
The correct option is **5, 4, 2, 1**.