Question

The correct increasing order of spin-only magnetic moment values of the complex ions:

[MnBr4]2− (A),
[Cu(H2O)6]2+ (B),
[Ni(CN)4]2− (C), and
[Ni(H2O)6]2+ (D)

is:

• A. A = B<C<D
• B. B<D<C
• C. C<B<A
• D. C<B<D<A

Hint:

For magnetic moment problems: 1. Determine oxidation state and \(d\)-electron count. 2. Identify ligand strength (weak field → high spin, strong field → low spin). 3. Count unpaired electrons and apply \(\mu = \sqrt{n(n+2)}\).

Answer 1

The Correct Option is D

To determine the correct increasing order of spin-only magnetic moment values of the given complex ions, we need to understand the concept of magnetic moments in coordination chemistry. The spin-only magnetic moment for a complex is given by the formula:

\[\mu = \sqrt{n(n+2)} \, \text{Bohr Magneton (B.M.)}\]

where n is the number of unpaired electrons in the complex. Let us analyze each complex ion:

1. [MnBr₄]²⁻ (A): Mn in this complex is in +2 oxidation state. Electronic configuration of Mn²⁺ is [Ar] 3d⁵, which means there are 5 unpaired electrons. Therefore, the spin-only magnetic moment is \[\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \, \text{B.M.}\].
2. [Cu(H₂O)₆]²⁺ (B): Cu in this complex is in +2 oxidation state. Electronic configuration of Cu²⁺ is [Ar] 3d⁹, which means there is 1 unpaired electron. Therefore, the spin-only magnetic moment is \[\mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \, \text{B.M.}\].
3. [Ni(CN)₄]²⁻ (C): Ni in this complex is in +2 oxidation state, and CN⁻ is a strong field ligand causing pairing of electrons. Hence, the electronic configuration is [Ar] 3d¹⁰, and there are 0 unpaired electrons. Therefore, the spin-only magnetic moment is \[\mu = \sqrt{0(0+2)} = 0 \, \text{B.M.}\].
4. [Ni(H₂O)₆]²⁺ (D): Ni in this complex is in +2 oxidation state. The electronic configuration of Ni²⁺ is [Ar] 3d⁸ with 2 unpaired electrons. Therefore, the spin-only magnetic moment is \[\mu = \sqrt{2(2+2)} = \sqrt{8} \approx 2.83 \, \text{B.M.}\].

Thus, the increasing order of spin-only magnetic moments is:

C < B < D < A

This matches the given correct answer.