Which of the following electronic configuration have the highest exchange energy :-

Options

A.
B.
C.
D.

Answer

To determine which electronic configuration has the highest exchange energy, we need to analyze the stability of the configurations based on their filling of orbitals. Exchange energy is directly related to the stability of the electronic configuration, which is higher for half-filled and fully filled configurations.

### Step-by-Step Solution:

1. **Understand Exchange Energy**:
- Exchange energy is a concept in quantum mechanics that relates to the stability of an electronic configuration. It is higher for configurations that are either half-filled or fully filled.

2. **Identify Half-Filled and Fully Filled Configurations**:
- A half-filled configuration occurs when orbitals are filled with one electron each before pairing begins. For example, in the d-orbitals, a half-filled configuration would be \(3d^5\).
- A fully filled configuration occurs when all orbitals in a subshell are completely filled. For the d-orbitals, this would be \(3d^{10}\).

3. **Evaluate the Given Options**:
- Let's assume we have the following configurations to analyze:
- Option A: \(3d^9\)
- Option B: \(3d^{10}\)
- Option C: \(3d^5\)
- Here, \(3d^{10}\) is fully filled, \(3d^5\) is half-filled, and \(3d^9\) is neither.

4. **Determine Stability**:
- The fully filled configuration (\(3d^{10}\)) is more stable than the half-filled configuration (\(3d^5\)).
- The half-filled configuration (\(3d^5\)) is more stable than the partially filled configuration (\(3d^9\)).

5. **Conclusion**:
- Since fully filled configurations have the highest stability, they also have the highest exchange energy. Therefore, among the options provided, the configuration with the highest exchange energy is \(3d^{10}\).

### Final Answer:
- The electronic configuration with the highest exchange energy is **Option B: \(3d^{10}\)**.