Which of the following have same magnetic moment

Options

A. `[Cr(H_2O)_6]^(2+)], [Fe(H_2O)_6]^(2+)`
B. `[Cr(H_2O)_6]^(2+)], [CoCl_6]^(2-)`
C. `[Cr(H_2O)_6]^(2+)], [CoCl_4]^(2-)`
D. `[Co(H_2O)_6]^(2+)], [Fe(H_2O)_6]^(2+)`

Answer

To determine which of the given complexes have the same magnetic moment, we need to calculate the number of unpaired electrons in each complex. The magnetic moment (μ) can be calculated using the formula:

\[ \mu = \sqrt{n(n + 2)} \]

where \(n\) is the number of unpaired electrons. If two complexes have the same number of unpaired electrons, they will have the same magnetic moment.

### Step-by-Step Solution:

**Step 1: Analyze the first option (Chromium and Iron).**
- **Chromium (Cr):**
- Electronic configuration: \( [Ar] 3d^5 4s^1 \)
- In +2 oxidation state: \( 3d^4 \) (loses 2 electrons from 4s and 1 from 3d)
- Number of unpaired electrons: 4 (as the 3d subshell has 4 unpaired electrons).

- **Iron (Fe):**
- Electronic configuration: \( [Ar] 3d^6 4s^2 \)
- In +2 oxidation state: \( 3d^6 4s^0 \)
- Number of unpaired electrons: 4 (as the 3d subshell has 4 unpaired electrons).

**Conclusion for Option 1:** Both Chromium and Iron have 4 unpaired electrons, so they have the same magnetic moment.

**Step 2: Analyze the second option (Chromium and Cobalt).**
- **Chromium (Cr):**
- In +2 oxidation state: 4 unpaired electrons (as calculated above).

- **Cobalt (Co):**
- Electronic configuration: \( [Ar] 3d^7 4s^2 \)
- In +4 oxidation state: \( 3d^5 \)
- Number of unpaired electrons: 5.

**Conclusion for Option 2:** Chromium has 4 unpaired electrons, while Cobalt has 5 unpaired electrons. They have different magnetic moments.

**Step 3: Analyze the third option (Chromium and Cobalt).**
- **Chromium (Cr):**
- In +2 oxidation state: 4 unpaired electrons (as calculated above).

- **Cobalt (Co):**
- In +2 oxidation state: \( 3d^7 4s^0 \)
- Number of unpaired electrons: 3.

**Conclusion for Option 3:** Chromium has 4 unpaired electrons, while Cobalt has 3 unpaired electrons. They have different magnetic moments.

**Step 4: Analyze the fourth option (Cobalt and Iron).**
- **Cobalt (Co):**
- In +2 oxidation state: 3 unpaired electrons (as calculated above).

- **Iron (Fe):**
- In +2 oxidation state: 4 unpaired electrons (as calculated above).

**Conclusion for Option 4:** Cobalt has 3 unpaired electrons, while Iron has 4 unpaired electrons. They have different magnetic moments.

### Final Conclusion:
The only pair of complexes that have the same magnetic moment is found in **Option 1** (Chromium and Iron).