The pair having the same magnetic moment is
[at. No. `Cr = 24, Mn = 25, Fe = 26 " and " Co = 27]`

Options

A. `[Cr(H_(2)O)_(6)]^(2+) and [Fe(H_(2)O)_(6)]^(2+)`
B. `[Mn(H_(2)O)_(6)]^(2+) nd [Cr(H_(2)O)_(6)]^(2+)`
C. `[CoCl_(4)]^(2-) and [Fe(H_(2)O)_(6)]^(2+)`
D. `[Cr(H_(2)O)_(6)]^(2+) and [CoCl_(4)]^(2-)`

Answer

To determine the pair of coordination compounds that have the same magnetic moment, we need to analyze the oxidation states and the number of unpaired electrons in each metal ion. Here's a step-by-step solution:

### Step 1: Identify the Coordination Compounds
The given coordination compounds are:
1. Cr(H₂O)₆²⁺
2. Fe(H₂O)₆²⁺
3. CoCl₄²⁻
4. Mn(H₂O)₆²⁺

### Step 2: Determine the Oxidation States
- For Cr(H₂O)₆²⁺: The oxidation state of Cr is +2.
- For Fe(H₂O)₆²⁺: The oxidation state of Fe is +2.
- For CoCl₄²⁻: The oxidation state of Co can be calculated as follows:
Let the oxidation state of Co be x. The total charge from 4 Cl⁻ is -4. Therefore, x - 4 = -2, leading to x = +2.
- For Mn(H₂O)₆²⁺: The oxidation state of Mn is +2.

### Step 3: Determine the Electron Configurations
Now, we find the electron configurations for each metal ion in the +2 oxidation state:
- Cr²⁺: The electron configuration is [Ar] 3d⁴ (4 unpaired electrons).
- Fe²⁺: The electron configuration is [Ar] 3d⁶ (4 unpaired electrons).
- Co²⁺: The electron configuration is [Ar] 3d⁷ (3 unpaired electrons).
- Mn²⁺: The electron configuration is [Ar] 3d⁵ (5 unpaired electrons).

### Step 4: Count the Number of Unpaired Electrons
- Cr²⁺: 4 unpaired electrons.
- Fe²⁺: 4 unpaired electrons.
- Co²⁺: 3 unpaired electrons.
- Mn²⁺: 5 unpaired electrons.

### Step 5: Determine Magnetic Moments
The magnetic moment (μ) can be calculated using the formula:
\[ μ = \sqrt{n(n + 2)} \]
where n is the number of unpaired electrons.

- For Cr²⁺:
\[ μ = \sqrt{4(4 + 2)} = \sqrt{24} \]
- For Fe²⁺:
\[ μ = \sqrt{4(4 + 2)} = \sqrt{24} \]
- For Co²⁺:
\[ μ = \sqrt{3(3 + 2)} = \sqrt{15} \]
- For Mn²⁺:
\[ μ = \sqrt{5(5 + 2)} = \sqrt{35} \]

### Step 6: Conclusion
The pairs that have the same magnetic moment are:
- Cr(H₂O)₆²⁺ and Fe(H₂O)₆²⁺, both having 4 unpaired electrons and the same magnetic moment.

### Final Answer
The pair having the same magnetic moment is:
**Cr(H₂O)₆²⁺ and Fe(H₂O)₆²⁺.**

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