Question

Which of the following pair of ions have same para magnetic moment? (a) \(\mathrm{Cu}^{2+}, \mathrm{Ti}^{3+}\) (b) \(\mathrm{Ti}^{3+}, \mathrm{Ni}^{2+}\) (c) \(\mathrm{Ti}^{4+}, \mathrm{Cu}^{2+}\) (d) \(\mathrm{Mn}^{2+}, \mathrm{Cu}^{2+}\)

Short answer

The pair \( \mathrm{Cu}^{2+} \) and \( \mathrm{Ti}^{3+} \) have the same paramagnetic moment.

Step-by-step solution

Understanding Paramagnetic Moment

The paramagnetic moment of an ion is determined by the number of unpaired electrons it has. The formula for the magnetic moment B is given by B = \sqrt{n(n+2)} \text{ Bohr Magnetons (BM)}, where \( n \) is the number of unpaired electrons.

Determine Unpaired Electrons for Each Ion

Identify the electronic configuration and count the unpaired electrons for each ion: - \( \mathrm{Cu}^{2+} \) has an electron configuration of 3d^9, thus 1 unpaired electron.- \( \mathrm{Ti}^{3+} \) has an electron configuration of 3d^1, thus 1 unpaired electron.- \( \mathrm{Ni}^{2+} \) has an electron configuration of 3d^8, thus 2 unpaired electrons.- \( \mathrm{Ti}^{4+} \) has an electron configuration of 3d^0, thus 0 unpaired electrons.- \( \mathrm{Mn}^{2+} \) has an electron configuration of 3d^5, thus 5 unpaired electrons.

Calculate Paramagnetic Moment for Each Ion

Use the formula \( \mu = \sqrt{n(n+2)} \) to calculate the magnetic moment for each ion:- For \( \mathrm{Cu}^{2+} \) and \( \mathrm{Ti}^{3+} \), \( \mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \text{ BM} \)- For \( \mathrm{Ni}^{2+} \), \( \mu = \sqrt{2(2+2)} = \sqrt{8} \approx 2.83 \text{ BM} \)- For \( \mathrm{Mn}^{2+} \), \( \mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \text{ BM} \)- For \( \mathrm{Ti}^{4+} \), \( \mu = 0 \text{ BM} \)

Compare Paramagnetic Moments

From the calculations, the ions \( \mathrm{Cu}^{2+} \) and \( \mathrm{Ti}^{3+} \) both have a magnetic moment of approximately 1.73 Bohr Magnetons. Therefore, this pair has the same paramagnetic moment.

Key concepts

Unpaired Electrons

Unpaired electrons are crucial in understanding the magnetic properties of atoms and ions. They are electrons that occupy orbitals singly instead of in pairs. The presence of unpaired electrons tends to generate a magnetic moment, resulting in paramagnetism. Paramagnetism refers to the tendency of these substances to be attracted by external magnetic fields.

The more unpaired electrons an ion has, the stronger its paramagnetic character tends to be. Transition metals, which often have partially filled d or f orbitals, typically have unpaired electrons. For example, Cu\(^{2+}\) has an electronic configuration of 3d\(^{9}\), which results in one unpaired electron. Similarly, Ti\(^{3+}\) with a configuration of 3d\(^{1}\) also has one unpaired electron.

Knowing how to determine the number of unpaired electrons can help in predicting the magnetic properties of an ion. In any given element, the number of unpaired electrons is deduced from its electronic configuration by writing down its electron distribution across different orbitals.

Magnetic Moment Formula

The magnetic moment formula is an essential tool in quantifying the magnetic strength of an ion. The formula given by \( \mu = \sqrt{n(n+2)} \), where \( \mu \) is the magnetic moment in Bohr magnetons (BM), and \( n \) is the number of unpaired electrons, allows us to calculate this property.

When applied in practice, this formula can help determine which ions have similar or different magnetic properties. For instance, both Cu\(^{2+}\) and Ti\(^{3+}\) ions, each having one unpaired electron, yield a magnetic moment of \( \mu = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73 \text{ BM} \).

This formula is particularly useful in distinguishing paramagnetic substances from one another. It not only allows us to identify the degree of paramagnetism but also predict how strongly a particular ion might react in the presence of a magnetic field. Calculating using this formula provides a clearer picture of how closely related certain ions might be regarding their paramagnetic characteristics.

Paramagnetism in Transition Metals

Transition metals are well-known for their paramagnetic properties due to their incompletely filled d subshells, which provide unpaired electrons. Paramagnetism in these metals and their ions arises because unpaired electrons align with external magnetic fields, generating a net magnetic moment.

In transition metal ions like Cu\(^{2+}\) and Ti\(^{3+}\), the unpaired d electrons play a significant role in producing these magnetic effects. Their electronic configurations, 3d\(^{9}\) and 3d\(^{1}\) respectively, help us understand the source of paramagnetism. Unlike in completely filled orbitals where electrons are paired and cancel each other's magnetism, partly filled orbitals manifest magnetism due to unpaired electrons.

Understanding paramagnetism in transition metals is vital for various applications, such as in catalyst design and magnetic resonance imaging (MRI). Engineering materials with tailored magnetic properties often relies on controlling the presence and behavior of unpaired electrons in transition metal ions.