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. Mn > Cr > Fe > Co
B. Cr > Fe > Mn > Co
C. Fe > Mn > Cr > Co
D. Cr > Mn > Fe > Co

Answer

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 can follow these steps:

### Step 1: Identify the Electronic Configurations
1. **Chromium (Cr)**: Atomic number = 24
- Electronic configuration: \( [Ar] 3d^5 4s^1 \)

2. **Manganese (Mn)**: Atomic number = 25
- Electronic configuration: \( [Ar] 3d^5 4s^2 \)

3. **Iron (Fe)**: Atomic number = 26
- Electronic configuration: \( [Ar] 3d^6 4s^2 \)

4. **Cobalt (Co)**: Atomic number = 27
- Electronic configuration: \( [Ar] 3d^7 4s^2 \)

### Step 2: Analyze the Stability of the Oxidation States
- When these metals lose two electrons to form \( M^{2+} \), we need to consider their electronic configurations after losing the electrons.

1. **For Manganese (Mn)**:
- Loses 2 electrons: \( 3d^5 4s^2 \) → \( 3d^5 \) (half-filled, stable configuration)

2. **For Chromium (Cr)**:
- Loses 2 electrons: \( 3d^5 4s^1 \) → \( 3d^4 4s^0 \) (less stable than Mn)

3. **For Iron (Fe)**:
- Loses 2 electrons: \( 3d^6 4s^2 \) → \( 3d^6 4s^0 \) (stable but not as favorable as Mn)

4. **For Cobalt (Co)**:
- Loses 2 electrons: \( 3d^7 4s^2 \) → \( 3d^7 4s^0 \) (least favorable)

### Step 3: Determine the Order of Ease of Losing Electrons
- The ease of losing electrons generally decreases as we move from left to right in the periodic table due to increasing nuclear charge and decreasing atomic size.
- Therefore, the order of ease of losing two electrons is:
1. **Manganese (Mn)** - most favorable due to half-filled configuration.
2. **Chromium (Cr)** - larger atomic size allows easier loss than Fe and Co.
3. **Iron (Fe)** - less favorable than Cr but more than Co.
4. **Cobalt (Co)** - least favorable.

### Step 4: Write the Final Order
Thus, the correct order of \( E^{\circ}_{M^{2+}/M} \) values with a negative sign is:
- **Mn > Cr > Fe > Co**

### Conclusion
The correct order is: **Manganese (Mn), Chromium (Cr), Iron (Fe), Cobalt (Co)**.