Problem 167 - A Complete Resource Book in Chemistry for JEE Main

Question

The 'spin-only' magnetic moment [in units of Bohr magneton \(\left.\left(\mu_{\mathrm{B}}\right)\right]\) of \(\mathrm{Ni}^{2+}\) in aqueous solution would be (Atomic number of \(\mathrm{Ni}=28\) ) (a) \(2.84\) (b) \(4.90\) (c) 0 (d) \(1.73\)

Step-by-Step Solution

Answer

The spin-only magnetic moment of \(\mathrm{Ni}^{2+}\) is approximately \(2.84\), matching option (a).

Step 1: Determine Electronic Configuration

The first step is to find the electron configuration of \( \text{Ni}^{2+} \). Nickel has an atomic number of 28, so its electron configuration is \( [\text{Ar}] \, 3d^8 \, 4s^2 \). However, since it loses 2 electrons to become \( \text{Ni}^{2+} \), the configuration is \( [\text{Ar}] \, 3d^8 \).

Step 2: Identify Unpaired Electrons

In the \(3d^8\) configuration of \( \text{Ni}^{2+} \), the five \(d\) orbitals are filled sequentially. The electrons will pair up as much as possible, but there are still 2 unpaired electrons (since there are 8 electrons for 5 orbitals and the first pair of electrons are placed one per orbital before pairing).

Step 3: Calculate Spin-Only Magnetic Moment

The spin-only magnetic moment \( \mu \) can be calculated using the formula: \( \mu = \sqrt{n(n+2)} \), where \( n \) is the number of unpaired electrons. For \( \text{Ni}^{2+} \), \( n = 2 \). Substituting \( n = 2 \) into the formula gives \[ \mu = \sqrt{2(2+2)} = \sqrt{8} = 2.828 \approx 2.84 \].

Step 4: Choose Correct Option

Compare the calculated magnetic moment with the given options. The calculated spin-only magnetic moment is approximately \(2.84\), which matches option (a).

Key Concepts

Electronic Configuration

Understanding the electronic configuration of an atom or ion is essential to predict its chemical behavior, including its magnetic properties. For the nickel atom (Ni), which has an atomic number of 28, this configuration is written as \([ ext{Ar}] \, 3d^8 \, 4s^2\). This notation indicates that Ni has its first 18 electrons arranged like the noble gas Argon (Ar), and then the subsequent 10 electrons occupy the 3d and 4s orbitals. However, when Ni forms the \( \text{Ni}^{2+} \) ion, it loses two electrons, typically from the 4s orbital, resulting in the electron configuration \([\text{Ar}] \, 3d^8\). This configuration is crucial in understanding the number of unpaired electrons and thus the magnetic properties of the ion.

Unpaired Electrons

Unpaired electrons are significant because they contribute to the magnetic properties of a substance. In the case of \( \text{Ni}^{2+} \), with its electron configuration of \( 3d^8 \), the d orbitals are involved in determining the number of unpaired electrons. Nickel's d orbitals can each hold 2 electrons, and with 5 available d orbitals, electrons will fill these sequentially. Each orbital will first receive one electron before pairing begins. Consequently, in \( 3d^8 \), there are 2 unpaired electrons because 8 electrons are distributed to fill five orbitals, and two remain unpaired. These unpaired electrons are key to calculating the magnetic moment of the ion.

Bohr Magneton

The Bohr magneton is a fundamental unit for expressing the magnetic moment of an electron due to its spin and orbital angular momentum. It is named after Niels Bohr, a physicist who significantly contributed to atomic theory. The Bohr magneton is denoted by \( \mu_B \) and is approximately \(9.274 \times 10^{-24} \text{ A m}^2\) or \( \text{J/T} \). The spin-only magnetic moment formula, \( \mu = \sqrt{n(n+2)} \), where \(n\) is the number of unpaired electrons, is used to estimate the magnetic moment in terms of Bohr magnetons. For \( \text{Ni}^{2+} \), with 2 unpaired electrons, the calculated spin-only magnetic moment is about 2.84 Bohr magnetons.

Ni2+ Ion

The \( \text{Ni}^{2+} \) ion, often found in aqueous solutions, plays a significant role in various chemical and biological processes. This ion is formed when a neutral nickel atom loses two electrons, usually making it an influential component in catalysts and other complex structures. Its magnetic properties, influenced by the d orbital configuration, are analyzed using the concept of spin-only magnetic moments. The \( \text{Ni}^{2+} \) ion's specific 3d orbital configuration leads to 2 unpaired electrons, which results in a measurable magnetic moment. Recognizing these properties is crucial in fields ranging from material science to chemistry.