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 [2010]

Step-by-Step Solution

Answer

7 electrons with spin \\(-\\frac{1}{2}\\) can be present in the 4f subshell.

Step 1: Understand the Problem

We are asked to find the maximum number of electrons with a specific spin quantum number in the 4f subshell. The spin quantum number can either be \(-\frac{1}{2}\) or \(+\frac{1}{2}\). We need to determine how many electrons can have the spin quantum number \(-\frac{1}{2}\) in the 4f subshell.

Step 2: Determine the Number of Electrons in the 4f Subshell

The f subshell can hold a maximum of 14 electrons. This includes both spins (+-1/2 and +-1/2).

Step 3: Divide Electrons by Spin

Since the 4f subshell can hold 14 electrons, and electrons are evenly distributed between spins \(+\frac{1}{2}\) and \(-\frac{1}{2}\), the maximum number of electrons with the spin quantum number of \(-\frac{1}{2}\) will be half of the electrons present in the f orbital.

Step 4: Calculate the Maximum Number of Electrons with Spin -1/2

Divide the total number of electrons in the 4f subshell by 2 to find how many can have a spin of \(-\frac{1}{2}\). That is, \frac{14}{2} = 7\.

Key Concepts

4f subshell

The 4f subshell is a fascinating part of an atom's electron configuration. Occupying the fourth shell, the 4f subshell is part of the f block in the periodic table. This subshell comes into play typically in elements known as lanthanides. Comprised of 7 orbitals, each capable of housing 2 electrons, the 4f subshell can ultimately hold up to 14 electrons in total.

• Located in the fourth energy level.
• Each of its orbitals can hold up to 2 electrons.
• It is critical in the electron configuration of heavy elements, specifically the lanthanides.

These electrons add up significantly to properties like magnetic characteristics due to their complex electron cloud shapes. Understanding the electron holding capacity of the 4f subshell is crucial for deciphering the properties of some of the most unique elements on the periodic table.

electron configuration

Understanding electron configuration is essential for visualizing how electrons are arranged within an atom. This is important because it helps predict chemical bonding and properties. In essence, electron configuration details the arrangement of electrons around an atom's nucleus. Each electron occupies an orbital, and these orbitals are grouped into different subshells such as s, p, d, and f.

• The 4f subshell fits into the overall electron configuration as part of the larger f block.
• Each subshell has a defined capacity, with the 4f subshell holding up to 14 electrons.
• Electron configuration follows the Aufbau principle, filling from the lowest to the highest energy orbitals.

Sequence plays a key role, and usually follows the periodic table from left to right. For instance, the 4f subshell begins filing after the 5s and 4d subshells, making it particularly important in understanding lanthanides.

maximum number of electrons

Every subshell has a specific maximum number of electrons it can accommodate. In the context of the 4f subshell, it can hold a maximum of 14 electrons. This maximum capacity pertains to all f orbitals, composed of 7 different orientations, each holding 2 electrons.

• Each orbital within the subshell holds 2 electrons, one with a spin of +1/2 and the other with -1/2.
• Understanding these limits is crucial for depicting accurate electron configurations.

For an f subshell, located from the fourth energy level, its maximum electron capacity brings about unique magnetic and chemical properties found in the rare earth elements known as lanthanides. This capacity directly influences electron pairing and spin, and thus contributes significantly to the chemical behavior of these elements.

spin -1/2

Spin quantum numbers are vital in understanding the behavior of electrons in atoms. Each electron can have a spin of either +1/2 or -1/2. In a given subshell, electrons will fill up orbitals with all spins equally distributed whenever possible.

• Electrons can exist in two states within an orbital: spin up (+1/2) or spin down (-1/2).
• In the 4f subshell, with its capacity for 14 electrons, 7 can have the spin -1/2.
• Spin is a fundamental property, like charge or mass.

The property of having spin -1/2 is notable because it contributes to the orbital magnetic moment. Particularly in the 4f subshell, electrons with spin -1/2 reveal much about the atom's magnetic characteristics and how these electrons can interact with their environment.