The order of increasing oxidation number of S in `S_(8),S_(2)O_(8)^(-2),S_(2)O_(3)^(2-),S_(4)O_(6)^(-2)` is given below -

Options

A. `S_(8)ltS_(2)O_(8)^(-2)ltS_(2)O_(3)^(2-)ltS_(4)O_(6)^(-2)`
B. `S_(2)O_(8)^(-2)ltS_(2)O_(3)^(-2)ltS_(4)O_(6)^(-2)ltS_(8)`
C. `S_(2)O_(8)^(-2)ltS_(8)ltS_(4)O_(6)^(2-)ltS_(2)O_(3)^(-2)`
D. `S_(8)ltS_(2)O_(3)^(2-)ltS_(4)O_(6)^(-2)ltS_(2)O_(8)^(-2)`

Explanation

To determine the order of increasing oxidation number of sulfur (S) in the compounds \( S_8, S_2O_8^{2-}, S_2O_3^{2-}, S_4O_6^{2-} \), we will calculate the oxidation state of sulfur in each compound step by step.

### Step 1: Calculate the oxidation state of sulfur in \( S_8 \)
- \( S_8 \) is the elemental form of sulfur.
- The oxidation number of sulfur in its elemental form is **0**.

### Step 2: Calculate the oxidation state of sulfur in \( S_2O_8^{2-} \)
- The formula is \( S_2O_8^{2-} \).
- Let the oxidation state of sulfur be \( x \).
- The oxidation state of oxygen is \(-2\).
- The equation can be set up as follows:
\[ 2x + 8(-2) = -2 \]
Simplifying this gives:
\[ 2x - 16 = -2 \\ 2x = 14 \\ x = +7 \]
- Therefore, the oxidation state of sulfur in \( S_2O_8^{2-} \) is **+7**.

### Step 3: Calculate the oxidation state of sulfur in \( S_2O_3^{2-} \)
- The formula is \( S_2O_3^{2-} \).
- Let the oxidation state of sulfur be \( x \).
- The equation can be set up as follows:
\[ 2x + 3(-2) = -2 \]
Simplifying this gives:
\[ 2x - 6 = -2 \\ 2x = 4 \\ x = +2 \]
- Therefore, the oxidation state of sulfur in \( S_2O_3^{2-} \) is **+2**.

### Step 4: Calculate the oxidation state of sulfur in \( S_4O_6^{2-} \)
- The formula is \( S_4O_6^{2-} \).
- Let the oxidation state of sulfur be \( x \).
- The equation can be set up as follows:
\[ 4x + 6(-2) = -2 \]
Simplifying this gives:
\[ 4x - 12 = -2 \\ 4x = 10 \\ x = 2.5 \]
- Therefore, the oxidation state of sulfur in \( S_4O_6^{2-} \) is **+2.5**.

### Step 5: Arrange the oxidation states in increasing order
- Now we have the oxidation states:
- \( S_8 \): 0
- \( S_2O_8^{2-} \): +7
- \( S_2O_3^{2-} \): +2
- \( S_4O_6^{2-} \): +2.5

- Arranging these in increasing order:
\[ S_8 (0) < S_2O_3^{2-} (+2) < S_4O_6^{2-} (+2.5) < S_2O_8^{2-} (+7) \]

### Final Answer
The order of increasing oxidation number of sulfur is:
\[ S_8 < S_2O_3^{2-} < S_4O_6^{2-} < S_2O_8^{2-} \]