The following facts are availabel `:`
`2A^(c-)+B_(2) rarr 2B^(-)+A_(2),`
`2C^(c-)+B_(2) rarr No reaction, `
`2D^(c-)+A_(2) rarr 2A^(c-)+D_(2)`
Which of the following statement is correct ?

Options

A. `E^(c-)._(C^(c-)|C_(2))gtE^(c-)._(B^(c-)|B_(2))gtE^(c-)._(A^(c-)|A_(2))gtE^(c-)._(D^(c-)|D_(2))`
B. `E^(c-)._(C^(c-)|C_(2))ltE^(c-)._(B^(c-)|B_(2))ltE^(c-)._(A^(c-)|A_(2))ltE^(c-)._(D^(c-)|D_(2))`
C. `E^(c-)._(C^(c-)|C_(2))ltE^(c-)._(B^(c-)|B_(2))gtE^(c-)._(A^(c-)|A_(2))gtE^(c-)._(D^(c-)|D_(2))`
D. `E^(c-)._(C^(c-)|C_(2))gtE^(c-)._(B^(c-)|B_(2))ltE^(c-)._(A^(c-)|A_(2))ltE^(c-)._(D^(c-)|D_(2))`

Explanation

To solve the problem, we need to analyze the given reactions and determine the standard oxidation potentials (E°) for the species involved. Let's break it down step by step.

### Step 1: Analyze the First Reaction
The first reaction is:
\[ 2A^{c-} + B_2 \rightarrow 2B^{-} + A_2 \]

In this reaction:
- \( B_2 \) is being reduced to \( B^{-} \).
- \( A^{c-} \) is being oxidized to \( A_2 \).

Since \( B_2 \) is reduced, it indicates that \( B_2 \) has a higher standard reduction potential compared to \( A^{c-} \). Therefore, we can conclude:
\[ E^{\circ} (A^{c-} \rightarrow A_2) < E^{\circ} (B^{-} \rightarrow B_2) \]

### Step 2: Analyze the Second Reaction
The second reaction is:
\[ 2C^{c-} + B_2 \rightarrow \text{No reaction} \]

Since there is no reaction, it implies that \( B_2 \) cannot oxidize \( C^{c-} \). This means:
\[ E^{\circ} (B^{-} \rightarrow B_2) < E^{\circ} (C^{c-} \rightarrow C_2) \]

### Step 3: Analyze the Third Reaction
The third reaction is:
\[ 2D^{c-} + A_2 \rightarrow D_2 + 2A^{c-} \]

In this case:
- \( A_2 \) is being reduced to \( A^{c-} \).
- \( D^{c-} \) is being oxidized to \( D_2 \).

This indicates that \( D^{c-} \) has a higher standard oxidation potential than \( A^{c-} \):
\[ E^{\circ} (D^{c-} \rightarrow D_2) > E^{\circ} (A^{c-} \rightarrow A_2) \]

### Step 4: Establish the Order of Standard Oxidation Potentials
From the analysis, we can summarize the relationships:
1. From the first reaction:
\[ E^{\circ} (A^{c-}) < E^{\circ} (B^{-}) \]
2. From the second reaction:
\[ E^{\circ} (B^{-}) < E^{\circ} (C^{c-}) \]
3. From the third reaction:
\[ E^{\circ} (D^{c-}) > E^{\circ} (A^{c-}) \]

Combining these relationships, we can establish the overall order of standard oxidation potentials:
\[ E^{\circ} (D^{c-}) > E^{\circ} (A^{c-}) > E^{\circ} (B^{-}) > E^{\circ} (C^{c-}) \]

### Conclusion
Based on the analysis, the correct statement regarding the standard oxidation potentials is:
- \( E^{\circ} (D^{c-}) > E^{\circ} (A^{c-}) > E^{\circ} (B^{-}) > E^{\circ} (C^{c-}) \)

### Final Answer
The correct option is **Option B**.