Problem 148 - A Complete Resource Book in Chemistry for JEE Main

Question

The outer electron configuration of Gd (atomic number \(=64\) ) is: (a) \(4 f^{7} 5 \mathrm{~d}^{1} 6 \mathrm{~s}^{2}\) (b) \(4 \mathrm{f}^{3} 5 \mathrm{~d}^{2} 6 \mathrm{~s}^{2}\) (c) \(4 \mathrm{f}^{5} 5 \mathrm{~d}^{0} 6 \mathrm{~s}^{2}\) (d) \(4 \mathrm{f}^{4} 5 \mathrm{~d}^{4} 6 \mathrm{~s}^{2}\)

Step-by-Step Solution

Answer

The correct outer electron configuration of Gd is (a) 4f⁷ 5d¹ 6s².

Step 1: Understand the Question

We need to determine the correct outer electron configuration of Gd (Gadolinium) with atomic number 64. This typically includes the electrons that are most involved in chemical reactions, located in the highest energy orbitals.

Step 2: Identify Electron Configuration Pattern

The electron configuration for Gd must account for 64 electrons. The general order for filling orbitals is based on increasing energy: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, and 6p.

Step 3: Calculate Electrons in Lower Energy Levels

Before reaching the outer electrons (4f, 5d, 6s), electrons fill lower energy levels: - 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² (18 electrons) - 3d¹⁰ 4p⁶ 5s² (20 electrons) - 4d¹⁰ 5p⁶ (18 electrons) Thus, 56 electrons fill these lower levels.

Step 4: Determine Remaining Outer Electron Configuration

After filling the lower energy levels ( 56 electrons), there are 64 - 56 = 8 electrons left for the outer orbitals (4f, 5d, 6s). The correct configuration prioritizes filling the 4f orbital then 5d and 6s: - 4f⁷ 5d¹ 6s².

Step 5: Match with Given Options

Compare the calculated outer electron configuration 4f⁷ 5d¹ 6s² with the given options: - (a) 4f⁷ 5d¹ 6s² - (b) 4f³ 5d² 6s² - (c) 4f⁵ 5d⁰ 6s² - (d) 4f⁴ 5d⁴ 6s² The correct configuration matches option (a).

Key Concepts

Gadolinium

Gadolinium is an intriguing element, symbolized as "Gd" with an atomic number of 64. It's one of the rare earth elements, nestled among a series of elements referred to as the lanthanides. These lanthanides are notable for their magnetic properties and are commonly used in various modern technologies, such as MRI machines and television screens.

In terms of electron configuration, gadolinium distinguishes itself with a specific arrangement of electrons. Out of its 64 electrons, the outermost configuration, known as the electron configuration, is crucial for understanding its chemical behavior. Gadolinium's unique electron configuration allows it to be involved in chemical reactions, and understanding this arrangement helps predict how gadolinium will interact with other elements. Thus, mastering the electron configuration of gadolinium is essential for those studying chemistry and physics applications involving rare earth metals.

f-block Elements

The f-block elements are also referred to as the lanthanides and actinides, and they include elements in which the 4f and 5f orbitals are being filled. These elements are often located separately at the bottom of the periodic table to maintain its compact shape despite their significant roles in chemistry.

Lanthanides, which include gadolinium, are characterized by filling up their 4f orbitals. These elements are intriguing because they display similar properties, making them difficult to separate. Additionally, their involvement in advanced technological applications, such as producing strong magnets and phosphors, emphasizes their importance.

• The electronic structure of these elements involves the addition of electrons to the f-orbital.
• These f-orbitals can hold up to 14 electrons, which is why the lanthanide series includes 15 elements, with 14 4f electrons.

Understanding the f-block elements is crucial for deeper insights into the periodic table and material science.

Orbital Filling Order

In chemistry, the order in which electrons occupy orbitals is critical for determining the electron configuration of an atom. This process is guided by several principles, including the Aufbau principle, Hund's rule, and the Pauli Exclusion Principle.

The general filling sequence starts with lower energy orbitals and progresses to higher energy orbitals. This is known as the Aufbau principle, which dictates that

• electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels.
• For example, the sequence follows: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, which helps determine the electron structure.

Hund's rule complements this by stating that electrons fill degenerate orbitals singly before pairing up. Lastly, the Pauli Exclusion Principle ensures that no two electrons in an atom have the same set of quantum numbers, essentially meaning each electron must have unique properties.

Understanding the orbital filling order is imperative for constructing accurate electron configurations and is a fundamental concept for learners diving into atomic theory and quantum chemistry.