Problem 149 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

An atom have \(\mathrm{d}^{8}\) configuration. The maximum number of electrons in the same spin is (a) 5 (b) 3 (c) 8 (d) 2

Step-by-Step Solution

Answer

The maximum number of electrons with the same spin in a \(\mathrm{d}^{8}\) configuration is (a) 5.

Step 1: Understanding Electron Configuration

The \(\mathrm{d}^{8}\) configuration indicates that there are 8 electrons in the d-subshell, which has 5 orbitals. Each orbital can hold up to 2 electrons with opposite spins.

Step 2: Applying Hund's Rule

According to Hund's rule, every orbital in a subshell is singly occupied with one electron before any orbital is doubly occupied. All electrons in singly occupied orbitals have the same spin.

Step 3: Determining Maximum Same Spin Electrons

To maximize the same spin electrons, fill each of the 5 d-orbitals with one electron first. This results in 5 electrons with the same spin. As there are 8 electrons in total, the remaining 3 will pair up with 3 of the 5 electrons already placed. Thus, the maximum number of electrons with the same spin is 5.

Key Concepts

Hund's Rule

Hund's Rule is a fundamental principle in atomic physics that helps us predict how electrons arrange themselves in a given subshell of an atom. According to Hund's Rule, electrons will fill orbitals in a way that maximizes the number of unpaired electrons, which results in the maximum total spin. To visualize this, imagine a set of empty seats in a theater. People would typically fill the seats by leaving as much space between each other as possible before someone starts sitting next to another. Similarly, electrons occupy separate orbitals in the same subshell before pairing up.

The reason behind this tendency is the repulsive force that electrons exert on each other due to their negative charges. By occupying different orbitals, they maintain the lowest energy configuration possible. In effect, Hund's Rule minimizes electron-electron repulsion and is crucial for determining electron configurations especially in complex atoms.

d-orbitals

The concept of d-orbitals plays a significant role in the arrangement of electrons within an atom. d-orbitals are a set of five orbitals, labeled as d_xy, d_xz, d_yz, d_x^2-y^2, and d_z^2. Each of these orbitals can hold a maximum of two electrons.

Unlike the more simplistic s and p orbitals, d-orbitals have a more complex shape that can be described as cloverleaf-shaped. Their orientation in space is crucial for understanding the chemical bonding and magnetic properties of transition metals, which have partially filled d-orbitals. The d-orbitals are also involved in forming metallic bonds and in the color of compounds, so a solid grasp of their nature and behavior is vital for advancing in chemistry.

Quantum Chemistry

Quantum Chemistry is the branch of chemistry that deals with the application of quantum mechanics to chemical systems. It's essentially the science of understanding chemical processes at the quantum level, which involves electrons and the nuclei of atoms.

In quantum chemistry, we delve into the Schrödinger equation, which describes how the quantum state of a physical system changes over time. This isn’t just an abstract concept – it directly affects how we predict and explain the structure of molecules, the rates of chemical reactions, and the energy changes associated with them. Quantum chemistry lies at the heart of many phenomena including the bonding between atoms, spectroscopy, and the behavior of materials at the molecular level.

Physical Chemistry

Physical Chemistry is the study of how matter behaves on a molecular and atomic level and how chemical reactions occur. It blends the principles of physics and chemistry to understand the physical properties of molecules, the forces that act upon them, and the energy changes that accompany these processes.

Within physical chemistry, there are several sub-disciplines, such as thermodynamics, kinetics, and quantum chemistry. It can involve studying the rate of a reaction, the interaction of molecules with light, or the calculation of equilibrium constants. A deep understanding of physical chemistry is essential for elucidating the fundamental aspects of chemical reactions and properties, thereby facilitating the design of new materials, pharmaceuticals, and energy solutions.