The atomic number of vanadium `(V)`, chromium `(Cr)`, manganese `(Mn)` and iron `(Fe)` are respectively `23,24,25,26`. Which out of these may be expected to have the jump in second ionisation enthalpy?

Options

A. `Mn`
B. `Fe`
C. `V`
D. `Cr`

Explanation

To determine which element among vanadium (V), chromium (Cr), manganese (Mn), and iron (Fe) has the highest jump in second ionization enthalpy, we will analyze the electronic configurations and the stability of the resulting ions after the first ionization.

### Step-by-Step Solution:

1. **Identify the Atomic Numbers and Write Electronic Configurations:**
- Vanadium (V, Z=23): \( \text{[Ar]} 4s^2 3d^3 \)
- Chromium (Cr, Z=24): \( \text{[Ar]} 4s^1 3d^5 \) (note the exception)
- Manganese (Mn, Z=25): \( \text{[Ar]} 4s^2 3d^5 \)
- Iron (Fe, Z=26): \( \text{[Ar]} 4s^2 3d^6 \)

2. **Understand the First Ionization Process:**
- The first ionization involves removing one electron from the outermost shell (4s orbital).
- For all elements, the first ionization will remove an electron from the 4s orbital.

3. **Analyze the Second Ionization Process:**
- After the first ionization, we need to consider the second ionization:
- **Vanadium (V)**: After removing one electron, it becomes \( \text{[Ar]} 4s^1 3d^3 \). The second ionization will remove an electron from the 4s orbital.
- **Chromium (Cr)**: After removing one electron, it becomes \( \text{[Ar]} 3d^5 \). The second ionization will remove an electron from the 3d orbital.
- **Manganese (Mn)**: After removing one electron, it becomes \( \text{[Ar]} 4s^1 3d^5 \). The second ionization will remove an electron from the 4s orbital.
- **Iron (Fe)**: After removing one electron, it becomes \( \text{[Ar]} 4s^1 3d^6 \). The second ionization will remove an electron from the 4s orbital.

4. **Evaluate Stability and Energy Requirements:**
- **Stability of the resulting ions**:
- For **V**, **Mn**, and **Fe**, the second ionization involves removing an electron from the 4s orbital, which is less stable compared to removing from a filled or half-filled d orbital.
- For **Cr**, after the first ionization, the second ionization involves removing an electron from a half-filled 3d orbital, which is more stable and requires more energy to remove.

5. **Conclusion:**
- The element that will show the highest jump in second ionization enthalpy is **Chromium (Cr)** because removing an electron from a half-filled d orbital (3d^5) requires significantly more energy than removing from the 4s orbital in the other elements.

### Final Answer:
The element that may be expected to have the jump in second ionization enthalpy is **Chromium (Cr)**.

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