Which statement is not true for the complex \(K_3[Fe(CN)_6]\)?

It is weakly repelled by external magnetic field

The correct answer is option 2. It is weakly repelled by external magnetic field.

Let us delve into each aspect of the complex \( K_3[Fe(CN)_6] \) to understand why the statement about it being "weakly repelled by an external magnetic field" is incorrect.

Complex Formation and Geometry

Complex: \( K_3[Fe(CN)_6] \)

Central Metal Ion: \( \text{Fe}^{3+} \)

Ligands: Cyanide ions (\( \text{CN}^- \))

In this complex, the central iron ion (\( \text{Fe}^{3+} \)) is surrounded by six cyanide ions. The cyanide ion is a strong field ligand, meaning it causes a significant splitting of the d-orbitals in the iron ion.

Electronic Configuration and Spin State

Oxidation State and d-Electrons: \( \text{Fe}^{3+} \) has an electronic configuration of \( [Ar] \, 3d^5 \).

Field Strength of Ligands: Cyanide ion (\( \text{CN}^- \)) is a strong field ligand, meaning it creates a large crystal field splitting energy (\(\Delta_0\)).

Low Spin Configuration: In the presence of a strong field ligand, the energy gap between the lower and upper sets of d-orbitals is large enough to pair up all the electrons in the lower energy set. This results in a low spin configuration where all electrons are paired. For \( \text{Fe}^{3+} \) in \( K_3[Fe(CN)_6] \), the d-electrons are paired due to the strong field effect of the cyanide ions.

Magnetic Properties

Diamagnetism vs. Paramagnetism: Diamagnetic materials have all their electrons paired and thus do not have a net magnetic moment. They are repelled by an external magnetic field, not attracted to it. Paramagnetic materials have unpaired electrons and are attracted to an external magnetic field.

For \( K_3[Fe(CN)_6] \): Because all electrons in \( \text{Fe}^{3+} \) are paired in this complex (due to the strong field cyanide ligands causing a low spin configuration), the complex is diamagnetic.

Behavior in a Magnetic Field: Since \( K_3[Fe(CN)_6] \) is diamagnetic, it is actually repelled by an external magnetic field rather than being weakly repelled. This is in contrast to weakly paramagnetic substances which are weakly attracted to an external magnetic field

Conclusion:

The statement "It is weakly repelled by an external magnetic field" is incorrect because \( K_3[Fe(CN)_6] \) is diamagnetic and should be described as repelled by the external magnetic field, not weakly but rather as a standard diamagnetic response.

Therefore, the correct answer to the question about which statement is not true for \( K_3[Fe(CN)_6] \) is indeed Option 2: "It is weakly repelled by external magnetic field."