Question

Predict the total spin in \(\mathrm{Ni}^{2+}\) ion (a) \(\pm 5 / 2\) (b) \(\pm 3 / 2\) (c) \(\pm 1 / 2\) (d) \(\pm 1\)

Short answer

The total spin of \( \mathrm{Ni}^{2+} \) is \( \pm 1 \) (option d).

Step-by-step solution

Determine the Electronic Configuration of Neutral Ni Atom

Nickel (Ni) has an atomic number of 28, which means a neutral Ni atom has 28 electrons. Its electron configuration is \( [ ext{Ar}] 3d^{8} 4s^{2} \).

Determine the Electron Configuration of Ni²⁺ Ion

In a \( ext{Ni}^{2+} \) ion, 2 electrons are removed. These are typically removed from the outermost shell, meaning the 4s electrons are lost first. Thus, the electron configuration for \( ext{Ni}^{2+} \) is \( [ ext{Ar}] 3d^{8} \).

Understand the Concept of Spin

Each electron contributes a spin of \( \pm \frac{1}{2} \). The total spin is the sum of the spins of all unpaired electrons in the atom or ion.

Find Unpaired Electrons in Ni²⁺

The \(3d\) subshell can hold up to 10 electrons, and with 8 electrons in the \(3d\) subshell for \( ext{Ni}^{2+} \), the configuration is \(3d^{8}\). This configuration results in 2 unpaired electrons.

Calculate Total Spin

With 2 unpaired electrons and the spin of each being \( \pm \frac{1}{2} \), the total spin \( S \) is calculated as \(2 \times \left(\frac{1}{2}\right) = 1\). Therefore, the total spin is \( \pm 1 \).

Identify the Correct Answer

The total spin for \( ext{Ni}^{2+} \) ion is \(\pm 1\), which corresponds to option (d).

Key concepts

Electronic Configuration

Every atom is composed of protons, neutrons, and electrons. Understanding how these electrons are arranged in the atom is crucial for determining many properties of the atom or ion. This arrangement is known as the electronic configuration. For a neutral nickel (Ni) atom, which has an atomic number of 28, there are 28 electrons distributed among different shells and subshells. The notation for its electronic configuration is \[ [\text{Ar}] 3d^{8} 4s^{2} \]. This configuration shows that after filling the 3d subshell with 8 electrons and the 4s subshell with 2, no electrons remain, illustrating the completed electron structure of a nickel atom. Understanding this is key to moving on to how electrons are removed in ionic forms.

Electron Removal

When an atom forms a positive ion, it loses electrons. In our case here with the \(\text{Ni}^{2+}\) ion, two electrons are removed from the neutral nickel atom. Removal of electrons typically starts from the outermost shell, which contains the highest energy electrons. For neutral nickel, this means removing electrons from the 4s orbital before the 3d. Therefore, the electron configuration of the \(\text{Ni}^{2+}\) ion is \[ [\text{Ar}] 3d^{8} \]. This change in the electronic configuration upon losing electrons is essential to understand, as it affects the chemical and physical properties of the ion.

Unpaired Electrons

In chemistry, unpaired electrons play a critical role in determining the magnetic and optical properties of an atom or ion. Electrons can be paired or unpaired, and it is crucial to identify unpaired electrons to understand an atom's total spin. For the \(3d^{8}\) electron configuration in the \(\text{Ni}^{2+}\) ion, the 3d subshell can hold up to 10 electrons. Having only 8 electrons leaves two of them unpaired. Finding these unpaired electrons involves understanding electron orbital filling and Hund's rule, where every orbital in the subshell gets one electron before any of them gets two. Identifying the number of unpaired electrons helps in determining the total spin.

Spin Quantum Number

The spin quantum number is a fundamental property of electrons, representing the angular momentum of an electron in its orbit. Each electron has a spin of either \(\frac{1}{2}\) or \(-\frac{1}{2}\). In the \(\text{Ni}^{2+}\) ion, which has 2 unpaired electrons, the spins can be either positive or negative. The total spin, denoted as \(S\), is given by the sum of the spins of all unpaired electrons. For example, with the two unpaired electrons in \(\text{Ni}^{2+}\), the total spin is calculated as \[ S = 2 \times \left(\frac{1}{2}\right) = 1 \]. Consequently, the total spin of the \(\text{Ni}^{2+}\) ion is \(\pm 1\), highlighting how unpaired electron spins contribute to the magnetic characteristics of ions.