Step 1: Determine the Oxidation State of Mn
Both complexes, [Mn(Br)6]³⁻ and [Mn(CN)6]³⁻, have an overall charge of -3. The ligands Br⁻ and CN⁻ are monodentate anions, each with a charge of -1. Let’s calculate the oxidation state of Mn.
For [Mn(Br)6]³⁻:
For [Mn(CN)6]³⁻:
Thus, Mn has an oxidation state of +3 in both complexes, a key concept for JEE Advanced coordination chemistry.
Step 2: Electron Configuration of Mn³⁺
The atomic number of Mn is 25, with an electronic configuration of:
For Mn³⁺, remove 2 electrons from 4s and 1 from 3d:
This d4 configuration is critical for determining the spin state and magnetic properties, a common topic in JEE Advanced inorganic chemistry.
Step 3: Nature of Ligands and Spin State
The nature of ligands determines whether the complex is high spin or low spin, a key concept in coordination compounds for JEE Advanced:
- Br⁻: Weak field ligand → high spin complex
- CN⁻: Strong field ligand → low spin complex
This distinction affects the electron arrangement and magnetic moment.
Step 4: Calculate Spin-Only Magnetic Moment
The spin-only magnetic moment ( ) is calculated using:
Where is the number of unpaired electrons.
For [Mn(Br)6]³⁻ (high spin, d⁴):
Electron arrangement in octahedral field:
This gives 4 unpaired electrons:
For [Mn(CN)6]³⁻ (low spin, d⁴):
Electron arrangement:
This gives 2 unpaired electrons:
These calculations align with JEE Advanced expectations for magnetic moment problems.
Step 5: Sum of Magnetic Moments
Add the magnetic moments of both complexes:
Final Answer: The sum of the spin-only magnetic moments is approximately 7 B.M.