Problem 71 - Chemistry The Central Science In Si Units

Question

What is the maximum number of electrons that can occupy each of the following subshells? (a) \(3 s,(\mathbf{b}) 2 p\), (c) \(4 d\) (d) \(5 \mathrm{~s}\).

Step-by-Step Solution

Answer

(a) 2 electrons, (b) 6 electrons, (c) 10 electrons, (d) 2 electrons.

Step 1: Understanding Subshells and Their Capacities

In atomic physics, each shell is divided into subshells designated by the letters s, p, d, and f. Each type of subshell has a characteristic number of orbitals that it can hold: s has 1 orbital, p has 3 orbitals, d has 5 orbitals, and f has 7 orbitals. Each orbital in turn can hold a maximum of 2 electrons.

Step 2: Determining Electron Capacity for 3s Subshell

The 3s subshell is an s-type, which contains 1 orbital. Since each orbital can hold 2 electrons, the maximum number of electrons in the 3s subshell is given by: \[ 1 ext{ orbital} imes 2 ext{ electrons/orbital} = 2 ext{ electrons} \]

Step 3: Determining Electron Capacity for 2p Subshell

The 2p subshell is a p-type, which contains 3 orbitals. Thus, the maximum number of electrons that the 2p subshell can accommodate is: \[ 3 ext{ orbitals} imes 2 ext{ electrons/orbital} = 6 ext{ electrons} \]

Step 4: Determining Electron Capacity for 4d Subshell

The 4d subshell is a d-type, containing 5 orbitals. Therefore, the maximum number of electrons for the 4d subshell is:\[ 5 ext{ orbitals} imes 2 ext{ electrons/orbital} = 10 ext{ electrons} \]

Step 5: Determining Electron Capacity for 5s Subshell

The 5s subshell is an s-type subshell, meaning it has 1 orbital. So, the maximum capacity for electrons here is:\[ 1 ext{ orbital} imes 2 ext{ electrons/orbital} = 2 ext{ electrons} \]

Key Concepts

Atomic Orbitals

Atoms are the building blocks of matter, and understanding their behavior is crucial to the study of chemistry and physics. At the core of atomic structure are atomic orbitals. These are regions in an atom where electrons are most likely to be found. You can think of orbitals as somewhat like rooms in a mansion where electrons reside. However, these room-like areas are not fixed in one specific location; they are more like clouds where the probability of finding an electron is highest.
Every orbital is defined by a set of quantum numbers, which include principal quantum number ( ), azimuthal quantum number ( ), magnetic quantum number ( ), and spin quantum number ( ). These numbers help in understanding the shape, size, and orientation of the orbitals. The concept of atomic orbitals is fundamental in sketching out how electrons are arranged in an atom. This arrangement is important because it affects an atom's chemical reactivity and properties like ionization energy and atomic radius.

Subshells

Subshells are subdivisions of electron shells based on their angular momentum quantum number. In simpler terms, a subshell is a grouping of orbitals within an energy level. Each shell of an atom is represented by a principal quantum number (n), and each n can contain one or more subshells.
Subshells are designated by the letters s, p, d, and f which stand for different shapes of orbitals within a given shell. For instance, the "s" subshell has spherical orbitals, "p" has dumbbell-shaped, "d" has more complex clover-shaped, and "f" has even more complex shapes. Each of these subshells has a different number of orbitals:

• s subshell has 1 orbital.
• p subshell has 3 orbitals.
• d subshell has 5 orbitals.
• f subshell has 7 orbitals.

Understanding subshells is essential for grasping how electrons fill different energy levels, which in turn informs us about the chemical bonding and properties of elements.

Electron Capacity

The concept of electron capacity is key to understanding how electrons fill subshells and orbitals within an atom. Each orbital can hold a maximum of two electrons. This is due to Pauli's Exclusion Principle, which states that no two electrons in the same atom can have the same set of four quantum numbers.
This means in practical terms, the maximum electron capacity for each type of subshell is determined by multiplying the number of orbitals it can hold by two. Hence, an "s" subshell, with 1 orbital, can hold up to 2 electrons (1 orbital × 2 electrons/orbital). A "p" subshell, with 3 orbitals, can hold up to 6 electrons (3 orbitals × 2 electrons/orbital). This pattern continues with "d" and "f" subshells, holding 10 and 14 electrons respectively.
Understanding the electron capacities of these subshells allows us to predict and explain the layout of an atom's electron configuration, especially when encountering different elements on the periodic table. This knowledge ultimately aids in comprehending the atom's chemical behavior.