The correct order of `E_(M^(2+)//M)^(@)` Values with negative sign for the four successive elements `Cr, Mn, Fe` and `Co` is:

Options

A. Fe gt Mn gt Cr gt Co
B. Cr gt Mn Fe gt Co
C. Mn gt Cr gt Fe gt Co
D. Cr gt Fe gt Mn gt Co

Explanation

To determine the correct order of \( E^{\circ}_{M^{2+}/M} \) values (with a negative sign) for the elements chromium (Cr), manganese (Mn), iron (Fe), and cobalt (Co), we need to analyze their oxidation potentials. The order can be derived from the general trends in the periodic table and the specific electronic configurations of these transition metals.

### Step-by-Step Solution:

1. **Identify the Electronic Configurations:**
- Chromium (Cr): \( [Ar] 3d^5 4s^1 \)
- Manganese (Mn): \( [Ar] 3d^5 4s^2 \)
- Iron (Fe): \( [Ar] 3d^6 4s^2 \)
- Cobalt (Co): \( [Ar] 3d^7 4s^2 \)

2. **Understand the Oxidation Potential:**
- The oxidation potential \( E^{\circ}_{M^{2+}/M} \) indicates how readily a metal can lose electrons to form \( M^{2+} \). A higher oxidation potential means the metal is more likely to oxidize.

3. **Trends in Oxidation Potential:**
- As we move from left to right across the transition metals, the effective nuclear charge increases, which generally increases the oxidation potential.
- However, manganese has a half-filled d-subshell configuration (3d^5), which is particularly stable. This stability makes it less likely to lose electrons compared to chromium, which has a less stable configuration (3d^4).

4. **Order of Oxidation Potentials:**
- Based on the above analysis, we can deduce the following order of oxidation potentials:
- Manganese (Mn) > Chromium (Cr) > Iron (Fe) > Cobalt (Co)

5. **Final Order with Negative Sign:**
- Since the question asks for the order of \( E^{\circ}_{M^{2+}/M} \) values with a negative sign, we can conclude that the order of oxidation potentials (which corresponds to the negative of the reduction potentials) is:
- Mn > Cr > Fe > Co

### Conclusion:
The correct order of \( E^{\circ}_{M^{2+}/M} \) values (with negative sign) for the elements Cr, Mn, Fe, and Co is:
\[ \text{Mn} > \text{Cr} > \text{Fe} > \text{Co} \]