Paramagnetic substances are those which attract the external magnetic field or which move from a weaker to stronger part of the magnetic field. Paramagnetic substances contain unpaired electrons. Diamagnetic substances are those which repel the external magnetic field or which tend to move away from stronger part to weaker part of the magnetic field. Diamagnetic substances are those which contain all paired electrons. Ferromagnetic substances are those which are attracted very strongly into the applied magnetic field. In ferromagnetic substances, the spins of all unpaired electrons and thus their magnetic moments are aligned in the same direction. Ferromagnetism is an extreme form of paramagnetism. Iron, Cobalt and Nickel are ferromagnetic substances. The magnetic property of a substance is due the spin angular momentum and orbital angular momentum of the electron and can be calculated using the formula

\[\mu_{S + L}= \sqrt{4S(S+1)+L(L+1)}BM\]

where S is the sum of spin quantum numbers of all electrons and L is the sum of orbital angular momentum quantum number. The unit of magnetic moment is Bohr magnetons (BM).

\[1 BM = \frac{eh}{4\pi m_e} = 9.237 × 10^{-21} \text{erg Gauss}^{-1}\]

In many compounds of 3d series metals, the magnetic moment due to orbital movement of electron is neglected as the orbital movement of these electrons is quenched by the surrounding species in compound or solution. The spin only magnetic moment can be calculated by using the spin only formula

\[\mu_s = \sqrt{n(n + 2)}BM\]

Which transition metal ion is diamagnetic?

Zn²⁺

The correct answer is option 4. \(Zn^{2+}\).

Let us delve into why Zn\(^{2+}\) ion is diamagnetic, while the others are paramagnetic:

Diamagnetism vs Paramagnetism:

Paramagnetism: Paramagnetic materials have unpaired electrons, resulting in a net magnetic moment. In transition metal ions, this occurs when there are one or more unpaired electrons in the \(3d\) orbital.

Diamagnetism: Diamagnetic materials have all electrons paired, resulting in no net magnetic moment. This occurs when there are no unpaired electrons or when the pairing of electrons in degenerate orbitals (like \(3d\) orbitals) is energetically favorable.

Analysis of Each Ion:

Co\(^{2+}\) (Cobalt ion in +2 oxidation state):

Neutral \(Co: [Ar] 3d^7 4s^2\)

Co\(^{2+}\): \([Ar] 3d^7\)

Configuration has 3 unpaired electrons making it paramagnetic.

Ni\(^{2+}\) (Nickel ion in +2 oxidation state):

Neutral \(Ni: [Ar] 3d^8 4s^2\)

Ni\(^{2+}\): \([Ar] 3d^8\)
Configuration has 2 unpaired electrons making it paramagnetic.

Cu\(^{2+}\) (Copper ion in +2 oxidation state):

Neutral \(Cu: [Ar] 3d^{10} 4s^1\)

Cu\(^{2+}\): \([Ar] 3d^9\)

Configuration has 1 unpaired electron, making it paramagnetic.

Zn\(^{2+}\) (Zinc ion in +2 oxidation state):

Neutral \(Zn: [Ar] 3d^{10} 4s^2\)

Zn\(^{2+}\): \([Ar] 3d^{10}\)

Configuration has all electrons paired, resulting in no unpaired electrons and therefore no net magnetic moment. This makes it diamagnetic.

Conclusion:

The key difference lies in the electron configuration:

Zn\(^{2+}\) has a filled \(3d^{10}\) configuration with all electrons paired, leading to diamagnetism.

Co\(^{2+}\), Ni\(^{2+}\), and Cu\(^{2+}\) have configurations with unpaired electrons (\(3d^7\), \(3d^8\), \(3d^9\) respectively), resulting in paramagnetism due to the presence of net magnetic moments from unpaired spins.

Therefore, Zn\(^{2+}\) is diamagnetic because all its electrons are paired in its \(3d^{10}\) configuration, leading to no net magnetic moment.