Problem 26 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following ions exhibit highest magnetic moment? (a) \(\mathrm{Cu}^{2+}\) (b) \(\mathrm{Ti}^{3+}\) (c) \(\mathrm{Ni}^{2+}\) (d) \(\mathrm{Mn}^{2+}\)

Step-by-Step Solution

Answer

The ion \(\mathrm{Mn}^{2+}\) exhibits the highest magnetic moment.

Step 1: Understand the Concept of Magnetic Moment

The magnetic moment of an ion is related to the number of unpaired electrons in its d-orbital. The magnetic moment in Bohr magnetons is given by the formula \(\mu_B = \sqrt{n(n+2)}\), where \(n\) is the number of unpaired electrons.

Step 2: Determine the Electron Configuration

Find the electron configuration for each ion to determine the number of unpaired electrons. - For \(\mathrm{Cu}^{2+}\): The electron configuration is \([\mathrm{Ar}] 3d^9\), with one unpaired electron.- For \(\mathrm{Ti}^{3+}\): The electron configuration is \([\mathrm{Ar}] 3d^1\), with one unpaired electron.- For \(\mathrm{Ni}^{2+}\): The electron configuration is \([\mathrm{Ar}] 3d^8\), with two unpaired electrons.- For \(\mathrm{Mn}^{2+}\): The electron configuration is \([\mathrm{Ar}] 3d^5\), with five unpaired electrons.

Step 3: Calculate the Magnetic Moment for Each Ion

Use the formula \(\mu_B = \sqrt{n(n+2)}\) for the magnetic moment.- \(\mathrm{Cu}^{2+}\): \(\mu_B = \sqrt{1(1+2)} = \sqrt{3}\)- \(\mathrm{Ti}^{3+}\): \(\mu_B = \sqrt{1(1+2)} = \sqrt{3}\)- \(\mathrm{Ni}^{2+}\): \(\mu_B = \sqrt{2(2+2)} = \sqrt{8}\)- \(\mathrm{Mn}^{2+}\): \(\mu_B = \sqrt{5(5+2)} = \sqrt{35}\)

Step 4: Compare the Magnetic Moments

Compare the magnetic moments calculated for each ion. The ion with the highest value of \(\mu_B\) has the highest magnetic moment. - \(\sqrt{3}\), \(\sqrt{3}\), \(\sqrt{8}\), \(\sqrt{35}\). Since \(\sqrt{35}\) is the largest value, \(\mathrm{Mn}^{2+}\) exhibits the highest magnetic moment.

Key Concepts

Unpaired Electrons

The concept of unpaired electrons is crucial when determining the magnetic properties of ions. When we discuss unpaired electrons, we are looking at electrons in an atom or ion that do not have a partner electron with an opposite spin in the same orbital. Electrons like to form pairs because it minimizes the energy of the system, leading to increased stability.
Unpaired electrons arise primarily in the d and f orbitals, where the number of electrons is not evenly distributed among the available orbitals. For example, in transition metal ions, missing electrons from d-orbitals can lead to the presence of unpaired electrons.

• The more unpaired electrons an ion has, the stronger its magnetic properties will be.
• This is because the unpaired electron spins contribute to the overall magnetic moment of the ion.

Understanding the number of unpaired electrons allows one to predict and calculate the magnetic moment of an ion, as an ion with many unpaired electrons, such as 8Mn^{2+}8, will exhibit a large magnetic moment.

Electron Configuration

Analyzing the electron configuration of an ion allows us to determine how many unpaired electrons are present. Electron configuration describes the arrangement of electrons in the electron shells and subshells: s, p, d, and f. Each shell has a specific capacity to hold electrons.
For transition metal ions, which often involve the d-subshells, predicting configuration requires removing electrons from the outermost s-orbitals first, followed by the d-orbitals.

• For 8Cu^{2+}8, the electron configuration is 8[Ar] 3d^98, where there is 1 unpaired electron.
• For 8Ti^{3+}8, it's 8[Ar] 3d^18, also with 1 unpaired electron.
• In 8Ni^{2+}8, we have 8[Ar] 3d^88, which gives us 2 unpaired electrons.
• 8Mn^{2+}8 has 8[Ar] 3d^58, highlighting the presence of 5 unpaired electrons.

Understanding electron configuration is an essential step toward figuring out both the chemical reactivity and magnetic nature of an ion.

Magnetic Properties of Ions

The magnetic properties of ions are deeply linked to the presence of unpaired electrons. An ion can exhibit diamagnetism or paramagnetism based on its electron configuration.
Diamagnetic ions have all their electrons paired, resulting in no net magnetic moment. In contrast, paramagnetic ions have one or more unpaired electrons and are attracted to magnetic fields.

• The more unpaired electrons present, the higher the magnetic moment and the greater the paramagnetism.
• The magnetic moment 81_B8 in Bohr magnetons is given by 81_B = 19n(n + 2)18, where 8n8 is the number of unpaired electrons.

By calculating the magnetic moment, we can compare ions to find out which has the strongest magnetic properties. For instance, 8Mn^{2+}8, with its 5 unpaired electrons, has a higher magnetic moment (843548) compared to the other ions, making it the most magnetic among the options provided.