Problem 143 - A Complete Resource Book in Chemistry for JEE Main

Question

The maximum number of \(4 \mathrm{f}\) electrons having spin quantum number \(-1 / 2\) is

Step-by-Step Solution

Answer

The maximum number of 4f electrons with spin -1/2 is 7.

Step 1: Understand the Electron Configuration

First, we need to understand where the 4f subshell is located in the electron configuration. The 4f subshell is part of the lanthanide series and contains a possible maximum of 14 electrons.

Step 2: Determine Half of the Electron Capacity

Each electron subshell consists of electrons that can have spins up (+1/2) or spins down (-1/2). Therefore, in any subshell, half of the electrons will have spin quantum number +1/2, and the other half will have -1/2.

Step 3: Calculate the Maximum Number of Electrons with Spin -1/2

Since the 4f subshell can hold a total of 14 electrons, the maximum number of these electrons that can have a spin quantum number of -1/2 will be half of 14, i.e., \[ \frac{14}{2} = 7 \].

Key Concepts

Spin Quantum Number

The spin quantum number is a fundamental property of electrons that describes their two possible orientations, often referred to as "spin up" and "spin down." We assign these orientations the values of "+1/2" and "-1/2," respectively. Electrons behave like tiny magnets because of their spin, and this property is essential for understanding how electrons are arranged in atoms. The Pauli Exclusion Principle plays a crucial role here. According to this principle, no two electrons in an atom can have the same set of quantum numbers. Therefore, in any given atomic subshell, electrons must have opposite spin orientations to occupy the same space. In simpler terms, if you have a subshell capable of holding a certain number of electrons, half of them will have a spin quantum number of "+1/2" and the other half "-1/2." For instance, in a 4f subshell, which can hold a maximum of fourteen electrons, seven will have a spin quantum number of "+1/2" and the other seven "-1/2." This equal distribution allows unique electron configurations that are critical in determining the chemical properties of elements.

Lanthanide Series

The lanthanide series is a group of 15 metallic elements, which range from lanthanum (La) to lutetium (Lu) in the periodic table and are characterized by the filling of the 4f electron subshell. These elements are sometimes referred to as rare earth elements. The 4f subshell is generally being filled as you move across this series. This gradual filling is responsible for the unique characteristics displayed by the lanthanides, including their magnetic and optical properties. Each element in the lanthanide series has slightly different electron configurations due to the increasing number of 4f electrons. Because the lanthanides have electrons filling the 4f orbitals, they show similarities in chemical behavior, making them quite distinct yet similar to each other in terms of reactivity and bonding properties. These properties are significant in applications such as magnets, phosphors, and catalysts, leveraging those specific characteristics that arise from the electron configuration of the 4f subshell.

Electron Subshells

Electron subshells are divisions of electron shells in an atom, composed of orbitals. These subshells are identified as s, p, d, and f, with each offering a different number of electron accommodation.

• s subshell: can hold up to 2 electrons
• p subshell: can hold up to 6 electrons
• d subshell: can hold up to 10 electrons
• f subshell: can hold up to 14 electrons

The f subshell, particularly the 4f subshell, is notable in the lanthanide series and can accommodate a maximum of 14 electrons. These electrons fill the f orbitals, which have complex shapes and are crucial for a variety of chemical properties. Understanding how subshells work helps explain the arrangement of electrons and the nature of the periodic table. It's important for predicting how atoms will interact in chemical reactions. The 4f subshells of the lanthanides fill up progressively, greatly impacting the magnetic and electronic behaviors of these elements.