Magnetic Moment

Step 1: Determine the oxidation state of Mn in each complex. - Both complexes have charge -3 and ligands Br and CN are monodentate anions with charge -1 each. For : Similarly, for : So, Mn is +3 in both complexes. Step 2: Determine the electronic configuration of . Atomic number of Mn = 25 Electronic configuration of Mn: For , remove 3 electrons: Step 3: Determine the nature of ligands and spin state. - Br is a weak field ligand → high spin complex - CN is a strong field ligand → low spin complex Step 4: Calculate spin only magnetic moment using formula: Where = number of unpaired electrons. For (high spin ): Electron arrangement: → 4 unpaired electrons For (low spin ): Electron arrangement: → 2 unpaired electrons Step 5: Sum of magnetic moments:

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.