Which of the following pairs of ions have the same electronic configuration ?

Options

A. `Cr^(3+) , Fe^(3+)`
B. `Fe^(3+),Mn^(2+)`
C. `Fe^(3+),Co^(3+)`
D. `Sc^(3+),Cr^(3+)`

Answer

To determine which pairs of ions have the same electronic configuration, we will first write the electronic configurations of the given ions. Let's break down the steps:

### Step 1: Identify the ions and their electronic configurations
We will write the electronic configurations for each of the ions mentioned in the question.

1. **Chromium (Cr)**:
- Atomic number = 24
- Electronic configuration: \( \text{[Ar]} \, 3d^5 \, 4s^1 \)
- For \( \text{Cr}^{3+} \):
- Remove 3 electrons (2 from 4s and 1 from 3d)
- Configuration: \( \text{[Ar]} \, 3d^3 \)

2. **Iron (Fe)**:
- Atomic number = 26
- Electronic configuration: \( \text{[Ar]} \, 4s^2 \, 3d^6 \)
- For \( \text{Fe}^{3+} \):
- Remove 3 electrons (2 from 4s and 1 from 3d)
- Configuration: \( \text{[Ar]} \, 3d^5 \)

3. **Manganese (Mn)**:
- Atomic number = 25
- Electronic configuration: \( \text{[Ar]} \, 4s^2 \, 3d^5 \)
- For \( \text{Mn}^{2+} \):
- Remove 2 electrons (2 from 4s)
- Configuration: \( \text{[Ar]} \, 3d^5 \)

4. **Cobalt (Co)**:
- Atomic number = 27
- Electronic configuration: \( \text{[Ar]} \, 4s^2 \, 3d^7 \)
- For \( \text{Co}^{3+} \):
- Remove 3 electrons (2 from 4s and 1 from 3d)
- Configuration: \( \text{[Ar]} \, 3d^6 \)

5. **Scandium (Sc)**:
- Atomic number = 21
- Electronic configuration: \( \text{[Ar]} \, 4s^2 \, 3d^1 \)
- For \( \text{Sc}^{3+} \):
- Remove 3 electrons (2 from 4s and 1 from 3d)
- Configuration: \( \text{[Ar]} \)

### Step 2: Compare the electronic configurations
Now, we will compare the electronic configurations of the ions:

- \( \text{Cr}^{3+} \): \( \text{[Ar]} \, 3d^3 \)
- \( \text{Fe}^{3+} \): \( \text{[Ar]} \, 3d^5 \)
- \( \text{Mn}^{2+} \): \( \text{[Ar]} \, 3d^5 \)
- \( \text{Co}^{3+} \): \( \text{[Ar]} \, 3d^6 \)
- \( \text{Sc}^{3+} \): \( \text{[Ar]} \)

From the above configurations, we can see that:

- \( \text{Fe}^{3+} \) and \( \text{Mn}^{2+} \) both have the electronic configuration of \( \text{[Ar]} \, 3d^5 \).

### Conclusion
The pair of ions that have the same electronic configuration is \( \text{Fe}^{3+} \) and \( \text{Mn}^{2+} \).

### Answer
**The correct option is B: \( \text{Fe}^{3+} \) and \( \text{Mn}^{2+} \)**.