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

Question

The outer electron configuration of Gd (atomic number \(=64\) ) is: (a) \(4 \mathrm{f}^{7} 5 \mathrm{~d}^{1} 6 \mathrm{~s}^{2}\) (b) \(4 \mathrm{f}^{\mathrm{s}} 5 \mathrm{~d}^{2} 6 \mathrm{~s}^{2}\) (c) \(4 f^{8} 5 \mathrm{~d}^{\circ} 6 \mathrm{~s}^{2}\) (d) \(4 \mathrm{f}^{4} 5 \mathrm{~d}^{4} 6 \mathrm{~s}^{2}\)

Step-by-Step Solution

Answer

The electron configuration of Gd is (a) \(4 \mathrm{f}^{7} 5 \mathrm{~d}^{1} 6 \mathrm{~s}^{2}\).

Step 1: Understand the Element

Gadolinium (Gd) has an atomic number of 64, indicating it has 64 electrons in its neutral state. It is part of the lanthanide series, which typically fills the 4f orbital.

Step 2: Determine Electron Configuration

The electron configuration of Gd, before considering electron anomalies (such as half-filled or fully filled subshell preferences), follows its position in the periodic table: - Begin with filling lower energy levels: \[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^6 \, 5s^2 \, 4d^{10} \, 5p^6 \, 6s^2 \, 4f^7 \, 5d^1 \] This gives a total of 64 electrons.

Step 3: Identify Exceptions for Gadolinium

For elements like gadolinium, which resides in the f-block, there can be exceptions based on the stability gained by having half-filled or fully filled subshells. Gd is known for its half-filled 4f subshell: \(4f^7\), accompanied by a single \(5d^1\) electron and the filled \(6s^2\) orbital for stability.

Step 4: Verify the Outer Electron Configuration

Based on the aspect of achieving a greater stability with a half-filled 4f subshell, the most stable configuration for gadolinium is \[ 4f^7 \, 5d^1 \, 6s^2 \] This matches option (a) in the given choices.

Key Concepts

Lanthanide Series

The lanthanide series, often referred to as the rare earth elements, encompasses 15 elements from lanthanum ( La ) to lutetium ( Lu ). These elements share similar properties and primarily fill the 4f subshell in their electron configurations. They are characterized by their shiny, silvery-white color and are known for their high magnetic and conductive properties, making them valuable in various industrial applications.
One key characteristic of the lanthanides is their progressive filling of the 4f orbitals. Starting from cerium ( Ce ) and continuing to lutetium, these electrons gradually fill the 4f subshell. Due to these similar electron configurations, the chemical reactivity across the series tends to be quite similar.
For students, understanding the lanthanide series is crucial when studying the periodic trends and properties of elements, especially when looking at atomic size, ionization energy, and other periodic properties.

Gadolinium

Gadolinium ( Gd ), with the atomic number 64, is a standout member of the lanthanide series. Known for its unique 4f^7 5d^1 6s^2 electron configuration, it highlights the concept of electron stability in half-filled subshells. Gadolinium possesses some unique properties due to its electron arrangement, particularly its magnetic attributes.
Gadolinium is often utilized in the medical field, primarily in magnetic resonance imaging (MRI) due to its excellent paramagnetic properties. This makes it particularly useful for enhancing image contrast and clarity.
Understanding gadolinium and its properties can enrich a student's comprehension of how subshell electron configurations affect chemical properties and technological applications.

4f Subshell

The 4f subshell is a critical region for the elements in the lanthanide series, as these orbitals are gradually filled from cerium to lutetium. The 4f orbitals possess a complex shape and can hold up to 14 electrons distributed across seven orbitals, with each capable of accommodating two electrons.
For students, visualizing this complex orbital is challenging but vital for comprehending electron configurations of lanthanide elements. Each electron added to the 4f subshell results in minute changes to the atomic radius and other chemical properties, illustrating the subtle influences of the f-block on element characteristics.
One notable aspect of the 4f subshell is its lower energy level compared to other nearby orbitals, such as 5d . This energy differentiation plays a significant role in determining the electron configuration and stability of the subshell.

Stability of Subshells

The concept of electron subshell stability is essential in chemistry, explaining why certain electron configurations are more energetically favorable than others. For subshells like the 4f , stability arises when there are either half-filled or fully filled electron states.
Half-filled subshells, such as 4f^7 in gadolinium, provide unique stability due to electron exchange and symmetry properties. This stability affects how elements like gadolinium arrange their electrons, preferring configurations that lower overall energy.
Some key points about subshell stability:

• Half-filled and fully filled subshells minimize electron repulsions and create symmetrical electron distributions, which are energetically favorable.
• This concept is not confined to the lanthanides and is observed across various elements in the periodic table.
• Understanding these stability principles helps students predict and explain electron configurations, and anticipate elemental behavior in chemical reactions.

For learners, mastering the idea of subshell stability provides vital insights into the trends and behaviors of elements, especially those found within the transition and lanthanide series.