Which one of the following ions exhibits the highest magnetic moment?

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

Let us break down how the magnetic moment of each ion is determined and why \(Mn^{2+}\) exhibits the highest magnetic moment:

Magnetic Moment Formula: The magnetic moment (\( \mu \)) of an ion is calculated using the formula:

\(\mu = \sqrt{n(n+2)} \text{ B.M.}\)

where \( n \) is the number of unpaired electrons. This formula is derived from the spin-only magnetic moment model, which considers the contribution of electron spin to the overall magnetic moment.

Analysis of Each Ion

1. \(Cu^{2+}\) (Copper(II))

Electronic Configuration of \(Cu\) at the ground state is \([Ar] 3d^{10} 4s^1\)

The electronic configuration of  \(Cu^{2+}\) is \([Ar] 3d^9\)

There is 1 unpaired electron in the 3d orbital.

\(\mu = \sqrt{1 \times (1 + 2)} = \sqrt{3} \approx 1.73 \text{ B.M.}\)

2. \(Ti^{3+}\) (Titanium(III))

Electronic Configuration of \(Ti\) at the ground state is \([Ar] 3d^2 4s^2\)

The electronic configuration of  \(Ti^{3+}\) is \([Ar] 3d^1\)

There is 1 unpaired electron in the 3d orbital.

\(\mu = \sqrt{1 \times (1 + 2)} = \sqrt{3} \approx 1.73 \text{ B.M.}\)

3. \(Ni^{2+}\) (Nickel(II))

Electronic Configuration of \(Ni\) at the ground state is \([Ar] 3d^8 4s^2\)

The electronic configuration of  \(Ni^{2+}\) is \([Ar] 3d^8\)

There are 2 unpaired electron in the 3d orbital.

\(\mu = \sqrt{2 \times (2 + 2)} = \sqrt{8} \approx 2.83 \text{ B.M.}\)

4. \(Mn^{2+}\) (Manganese(II))

Electronic Configuration of \(Mn\) at the ground state is \([Ar] 3d^5 4s^2\)

The electronic configuration of  \(Mn^{2+}\) is \([Ar] 3d^5\)

There are 5 unpaired electron in the 3d orbital.

\(\mu = \sqrt{5 \times (5 + 2)} = \sqrt{35} \approx 5.92 \text{ B.M.}\)

The magnetic moment of an ion is directly related to the number of unpaired electrons. More unpaired electrons result in a higher magnetic moment. Here’s why:

\(Mn^{2+}\) has the most unpaired electrons (5) among the ions listed, leading to the highest magnetic moment.

\(Ni^{2+}\) has 2 unpaired electrons, resulting in a lower magnetic moment than \(Mn^{2+}\).

\(Cu^{2+}\) and \(Ti^{3+}\) both have only 1 unpaired electron, resulting in the lowest magnetic moment among the options.

In summary, the magnetic moment increases with the number of unpaired electrons. Therefore, \(Mn^{2+}\) exhibits the highest magnetic moment due to having 5 unpaired electrons.