Problem 23 - Chemistry in 30 days

Question

A subshell with \(l=2\) is called (a) \(\mathrm{s}\) (b) \(\mathrm{p}\) (c) \(\mathrm{d}\) (d) \(\mathrm{f}\)

Step-by-Step Solution

Answer

The subshell with \( l=2 \) is called a \( \mathrm{d} \) subshell, so the answer is (c).

Step 1: Understanding Quantum Number l

The angular momentum quantum number, denoted as \( l \), defines the shape of an atomic orbital and can take integer values from 0 to \( n-1 \), where \( n \) is the principal quantum number. Each value of \( l \) corresponds to a different type of subshell.

Step 2: Identifying Subshells

The values of \( l \) are assigned to specific letters as follows:- If \( l = 0 \), the subshell is an \( \mathrm{s} \) subshell.- If \( l = 1 \), the subshell is a \( \mathrm{p} \) subshell.- If \( l = 2 \), the subshell is a \( \mathrm{d} \) subshell.- If \( l = 3 \), the subshell is an \( \mathrm{f} \) subshell.

Step 3: Solving the Problem

Given that \( l = 2 \), we can see from the above assignment that this corresponds to a \( \mathrm{d} \) subshell. Therefore, the correct answer is (c) \( \mathrm{d} \).

Key Concepts

Angular Momentum Quantum Number

The angular momentum quantum number, typically denoted by the letter \( l \), is an essential part of understanding atomic structure and electron configurations. It plays a critical role in determining the shape of atomic orbitals. For a given principal quantum number \( n \), \( l \) can have integer values ranging from 0 up to \( n-1 \). Each distinct \( l \) value represents a different kind of subshell within an atom, which significantly affects the way electrons are distributed around the nucleus.

• If \( l = 0 \), it corresponds to an \( \mathrm{s} \) subshell, which has a spherical shape.
• When \( l = 1 \), we have a \( \mathrm{p} \) subshell, often shaped like two teardrops pointing in opposite directions.
• \( l = 2 \) gives us a \( \mathrm{d} \) subshell, which has more complex shapes.
• Lastly, \( l = 3 \) corresponds to an \( \mathrm{f} \) subshell, known for even more intricate shapes.

Understanding \( l \) is crucial for predicting and explaining the chemical properties of elements.

Atomic Orbitals

Atomic orbitals are regions around an atom's nucleus where there is a high probability of finding electrons. These orbitals are described by a set of quantum numbers, including the angular momentum quantum number \( l \). Each orbital can hold a maximum of two electrons, provided they have opposite spins.
The principal quantum number \( n \) relates to the size and energy level of the orbital, but the angular momentum quantum number \( l \) influences the shape. As a result, orbitals with different values of \( l \) have distinct shapes and are named based on these values:

• \( \mathrm{s} \) orbitals (spherical) when \( l = 0 \)
• \( \mathrm{p} \) orbitals (dumbbell-shaped) when \( l = 1 \)
• \( \mathrm{d} \) orbitals (cloverleaf-shaped and more) when \( l = 2 \)
• \( \mathrm{f} \) orbitals (complex shaped structures) when \( l = 3 \)

The shape and orientation of these orbitals are critical for understanding how atoms form bonds in molecules.
These orbital configurations play a fundamental role in the chemical behavior and properties of atoms.

Subshell Identification

Identifying subshells is a vital part of understanding the layout of electrons within an atom. Each subshell is characterized by both the principal quantum number \( n \) and the angular momentum quantum number \( l \). This combination helps identify the specific orbital types within a given principal energy level.
In practice:

• \( n = 1 \) and \( l = 0 \) corresponds to the 1s subshell.
• \( n = 2 \) can have \( l = 0 \) and 1, yielding 2s and 2p subshells.
• \( n = 3 \) introduces \( l = 2 \), allowing for 3d subshells in addition to 3s and 3p.

This pattern continues, increasing the number of subshells as \( n \) increases. Understanding which subshell corresponds to a given \( l \) value helps in predicting electron distributions.
This knowledge provides insights into the atom's chemistry and its interactions with other atoms/molecules.
This is especially important for predicting the reactivity and bonding behavior of elements.