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Diamagnetism is a property of a substance that does not have any unpaired electrons in its electron configuration. When a substance is diamagnetic, it creates an induced magnetic field in the opposite direction of an externally applied magnetic field. This causes a very weak repulsion.
In the context of coordination complexes, a complex is considered diamagnetic if all of its electrons are paired in its d-orbitals. This typically happens when the d-orbitals are completely filled. For example, in the given problem, complexes like

• \([\mathrm{ZnBr}_{4}]^{2-}\)
• \([\mathrm{PtCl}_{4}]^{2-}\)
• and \(\mathrm{OsO}_{4}\)

are diamagnetic, as all their electrons are paired. Understanding diamagnetism in coordination complexes helps in predicting how these complexes will react in magnetic fields.

Paramagnetism occurs when a substance has one or more unpaired electrons in its electron configuration. Unlike diamagnetism, paramagnetic substances are attracted to an external magnetic field and as a result, align with it.
In coordination complexes, a paramagnetic complex typically contains unpaired electrons in its d-orbitals. This is caused by partially filled d-orbitals. For example, the complex \([\mathrm{Mn}(\mathrm{H}_{2} \mathrm{O})_{6}]^{3+}\) is paramagnetic because it has four unpaired electrons in its 3d orbitals.
Key characteristics of paramagnetic substances include:

• Presence of unpaired electrons
• Attraction to external magnetic fields
• Production of an induced magnetic field in the same direction as the external field

Recognizing paramagnetism in coordination complexes helps predict their behavior in magnetic fields, which is essential for various applications in chemistry and materials science.

An oxidation state, or oxidation number, is an indicator of the electron density or charge around an atom in a compound or complex. Determining the oxidation state is crucial for understanding the electron configuration and magnetic properties of a coordination complex.
For coordination complexes in the exercise:

• The \(\mathrm{Zn}\) in \([\mathrm{ZnBr}_{4}]^{2-}\) has an oxidation state of +2.
• The \(\mathrm{Mn}\) in \([\mathrm{Mn}(\mathrm{H}_{2} \mathrm{O})_{6}]^{3+}\) is in the +3 oxidation state.
• The \(\mathrm{Os}\) in \(\mathrm{OsO}_{4}\) has an oxidation state of +8.
• The \(\mathrm{Pt}\) in \([\mathrm{PtCl}_{4}]^{2-}\) has an oxidation state of +4.

The oxidation state provides insight into how electrons are distributed in a complex, which in turn, helps predict the geometry, reactivity, and magnetic properties of the complex. Knowing the oxidation state helps chemists in manipulating these properties for specific applications.

Electron configuration is the arrangement of electrons in an atom or ion within its atomic orbitals. This arrangement is crucial for determining the chemical behavior and magnetic properties of coordination complexes.
Each coordination complex in the exercise has different electron configurations due to varying oxidation states:

• For \(\mathrm{Zn}^{2+}\), \[1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10}\], all d-orbitals are filled, indicating diamagnetism.
• For \(\mathrm{Mn}^{3+}\), \[1s^2 2s^2 2p^6 3s^2 3p^6 3d^{4}\], there are unpaired electrons, leading to paramagnetism.
• For \(\mathrm{Os}^{8+}\), \[1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2 5p^6\], filled d-orbitals indicate diamagnetism.
• For \(\mathrm{Pt}^{4+}\), \[1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^2\], completely fills the d-orbitals, also showing diamagnetism.

Understanding electron configurations helps predict the stability, reactivity, and magnetic tendencies of coordination complexes, which is paramount in advancing chemical knowledge and its applications.