Problem 135 - A Complete Resource Book in Chemistry for JEE Main

Question

An ion of a d-block element has magnetic moment 5.92 BM select the ion among the following: (a) \(\mathrm{Sc}^{3+}\) (b) \(\mathrm{Zn}^{2+}\) (c) \(\mathrm{Mn}^{2+}\) (d) \(\mathrm{Cr}^{3+}\)

Step-by-Step Solution

Answer

The ion with the magnetic moment 5.92 BM is \( \text{Mn}^{2+} \).

Step 1: Understand the formula

The magnetic moment of an ion due to unpaired electrons is calculated using the formula: \( \mu = \sqrt{n(n+2)} \), where \( n \) is the number of unpaired electrons.

Step 2: Determine the number of unpaired electrons corresponding to the magnetic moment

The magnetic moment given is 5.92 BM. Using the formula \( \mu = \sqrt{n(n+2)} \), we solve for \( n \). The calculated magnetic moment of 5.92 BM corresponds to \( n = 5 \), which implies there are 5 unpaired electrons.

Step 3: Analyze the electron configuration of each ion

1. \( \text{Sc}^{3+} \): \([\text{Ar}] \), 0 unpaired electrons.2. \( \text{Zn}^{2+} \): \([\text{Ar}]3d^{10}\), 0 unpaired electrons.3. \( \text{Mn}^{2+} \): \([\text{Ar}]3d^5\), 5 unpaired electrons.4. \( \text{Cr}^{3+} \): \([\text{Ar}]3d^3\), 3 unpaired electrons.

Step 4: Select the ion with the correct number of unpaired electrons

Among the given ions, \( \text{Mn}^{2+} \) has 5 unpaired electrons, which matches the required condition as calculated from the magnetic moment formula \( \mu = 5.92\).

Key Concepts

Unpaired Electrons

Unpaired electrons play a crucial role in determining the magnetic properties of an element or ion. These electrons are those that are not paired with another electron with opposite spin in an atom's subshells. In simple terms, when electrons are singly occupied in their orbitals, they are considered unpaired.

Unpaired electrons contribute to the magnetic moment of a substance. A substance with more unpaired electrons will generally have a stronger magnetic moment, often making it paramagnetic. On the other hand, if all electrons in an atom or ion are paired, the magnetic fields generated cancel each other out, resulting in a non-magnetic material.

Because of these properties, understanding the count of unpaired electrons can help predict and explain the behavior of an ion or molecule in a magnetic field. This is why, in exercises like determining the magnetic moment of different ions, identifying the number of unpaired electrons is a crucial step.

Electron Configuration

Electron configuration is a way of representing the distribution of electrons across the orbitals of an atom or ion. It dictates the chemical properties and reactivity of elements by illustrating how electrons are arranged in atomic orbitals.

• The electron configuration notation consists of a series of numbers and letters (such as 1s, 2s, 2p, 3s, etc.) that indicate the energy levels, subshells, and number of electrons in those subshells.
• For ions, electron configurations are adjusted by removing or adding electrons to the outermost shell according to the ion's charge.

Examining an element's or ion's electron configuration can provide insights into its magnetic properties and stability. For instance, the electron configuration for \( Mn^{2+} is [Ar]3d^5\), which clearly shows it has five unpaired electrons in the 3d subshell, leading to its significant magnetic moment.

D-Block Elements

D-block elements, also known as transition metals, include those elements found in groups 3 through 12 of the periodic table. A unique characteristic of these elements is the filling of their 3d, 4d, or 5d orbitals. As a result, these elements exhibit distinct properties such as variable oxidation states and colored compounds.

The d-block elements demonstrate a unique ability to form ions with different charges due to the near equal energy level of 's' and 'd' orbitals. This results in diverse magnetic and chemical behavior, particularly due to the presence of unpaired electrons in the d-orbital.

• In these elements, the partially filled d orbitals permit electrons to remain unpaired, a necessary condition for magnetism.
• Their electron configurations significantly influence their magnetic moment and chemical reactivity.

Understanding the behavior of d-block elements involves closely examining their electron configurations to identify any unpaired electrons, which play a crucial role in determining their magnetic properties.