Which of the following compounds will be repelled when placed in an external magnetic field?

The correct option is: K₄[Fe(CN)₆]

Step-by-Step Explanation:

1. Magnetic Behavior of Coordination Compounds:
Compounds behave differently when placed in an external magnetic field depending on their electronic configurations:
- Paramagnetic substances: These contain one or more unpaired electrons and are weakly attracted by an external magnetic field.
- Diamagnetic substances: These have all of their electrons paired (no unpaired electrons) and are weakly repelled by an external magnetic field.
To identify which compound is repelled, we need to find the complex that is diamagnetic.

2. Analyzing the Oxidation State of Fe in K₄[Fe(CN)₆]:
First, we determine the oxidation state of the central metal atom, iron (Fe), in the coordination complex K₄[Fe(CN)₆]:
- K₄[Fe(CN)₆] dissociates to give four potassium cations and one complex anion:
K₄[Fe(CN)₆] → 4K⁺ + [Fe(CN)₆]^4-
- Let the oxidation state of Fe be x. Since CN^- is a monodentate anionic ligand with a -1 charge:
x + 6(-1) = -4
x - 6 = -4
x = +2
Thus, the iron ion is in the +2 oxidation state (Fe²⁺).

3. Electronic Configuration of Fe²⁺:
- The atomic number of Fe is 26, and its neutral ground-state electronic configuration is:
[Ar] 3d⁶ 4s²
- For the Fe²⁺ ion (formed by losing two 4s electrons), the configuration is:
[Ar] 3d⁶ 4s⁰

4. Splitting and Pairing of d-electrons:
- In the octahedral complex [Fe(CN)₆]^4-, the cyanide ion (CN^-) acts as a strong field ligand.
- According to Crystal Field Theory (CFT), strong field ligands produce a large crystal field splitting energy (Δ_o) that is greater than the pairing energy (P). This causes the 6 d-electrons of Fe²⁺ to pair up in the lower-energy t_2g orbitals instead of entering the higher-energy e_g orbitals.

The resulting distribution of the 6 electrons in the d-orbitals can be represented as:

$$t_{2g}^6{e}_g^0$$

Specifically, all three t_2g orbitals are completely filled with paired electrons: (↑↓, ↑↓, ↑↓).

5. Conclusion:
Since all 6 d-electrons in K₄[Fe(CN)₆] are paired, the number of unpaired electrons is zero (n = 0). Because it has no unpaired electrons, the compound is diamagnetic and will be repelled when placed in an external magnetic field.