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The magnetic moment of M^(2+) is 3.87 BM...

The magnetic moment of `M^(2+)` is 3.87 BM. The species is :

A

`Mn^(2+)`

B

`V^(2+)`

C

`Ti^(2+)`

D

`Cr^(2+)`

Text Solution

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The correct Answer is:
To determine the species corresponding to the magnetic moment of \( M^{2+} \) being 3.87 Bohr magneton (BM), we can follow these steps: ### Step 1: Identify the Element The magnetic moment is given as 3.87 BM. We need to consider common transition metals that can exist in a +2 oxidation state. ### Step 2: Determine the Ground State Electronic Configuration For manganese (Mn), the ground state electronic configuration is: - \( \text{Mn: } [Ar] 3d^5 4s^2 \) ### Step 3: Find the Configuration for \( M^{2+} \) When manganese loses two electrons to form \( Mn^{2+} \), the configuration becomes: - \( \text{Mn}^{2+}: 3d^5 \) ### Step 4: Calculate the Number of Unpaired Electrons In the \( 3d^5 \) configuration, all five electrons are unpaired (due to Hund's rule). Thus: - Number of unpaired electrons, \( n = 5 \) ### Step 5: Use the Formula for Magnetic Moment The formula for calculating the magnetic moment (\( \mu \)) is: \[ \mu = \sqrt{n(n + 2)} \] Substituting \( n = 5 \): \[ \mu = \sqrt{5(5 + 2)} = \sqrt{5 \times 7} = \sqrt{35} \approx 5.92 \text{ BM} \] This value is higher than the given magnetic moment, indicating that manganese is not the correct species. ### Step 6: Check Other Transition Metals Next, we check vanadium (V): - Ground state configuration: \( \text{V: } [Ar] 3d^3 4s^2 \) - For \( V^{2+} \): \( 3d^3 \) - Number of unpaired electrons in \( 3d^3 \): \( n = 3 \) Calculating the magnetic moment for \( V^{2+} \): \[ \mu = \sqrt{3(3 + 2)} = \sqrt{3 \times 5} = \sqrt{15} \approx 3.87 \text{ BM} \] This matches the given magnetic moment. ### Conclusion The species corresponding to the magnetic moment of \( M^{2+} = 3.87 \) BM is: - **Vanadium (V)** in the +2 oxidation state.
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Knowledge Check

  • The magnetic moment of xomplex ion is 2.83 BM. The complex ion is:

    A
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    They have different no. of d electrons
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