Question

List the four possible subshells in the quantum-mechanical model, the number of orbitals in each subshell, and the maximum number of electrons that can be contained in each subshell.

Short answer

The four subshells are s, p, d, and f, with 1, 3, 5, and 7 orbitals respectively, and can hold a maximum of 2, 6, 10, and 14 electrons respectively.

Step-by-step solution

Identify the Subshells

In the quantum-mechanical model of the atom, there are four types of subshells designated as s, p, d, and f. These subshells are determined by the angular momentum quantum number, l, which takes values from 0 to 3 for these subshells respectively.

Determine the Number of Orbitals

The number of orbitals in each subshell can be found using the formula 2l + 1, where l is the angular momentum quantum number corresponding to each subshell. The s subshell (l=0) has 1 orbital, the p subshell (l=1) has 3 orbitals, the d subshell (l=2) has 5 orbitals, and the f subshell (l=3) has 7 orbitals.

Calculate the Maximum Number of Electrons

The maximum number of electrons in a subshell is given by the formula 2(2l + 1). This arises from the fact that each orbital can hold a maximum of 2 electrons, one with spin up and one with spin down. Substituting the value of l for each subshell, we get that s subshell can hold up to 2 electrons, p subshell up to 6 electrons, d subshell up to 10 electrons, and f subshell up to 14 electrons.

Key concepts

Atomic Orbitals

At the heart of quantum chemistry lies the concept of atomic orbitals—mathematical functions that describe the probable locations of electrons in an atom. These orbitals are not physical spaces but rather zones with a high likelihood of finding an electron. In simple terms, they are like clouds around the nucleus where electrons are most likely to be.

Each orbital can house up to two electrons with opposite spins. The shape and orientation of these orbitals are defined by quantum numbers. The principal quantum number determines the energy level and size, while the other quantum numbers, which we'll explore next, define the shape and orientation of the orbitals.

Angular Momentum Quantum Number

Diving further into quantum numbers, we encounter the angular momentum quantum number, often symbolized by the letter 'l.' This number is crucial because it determines the shape of an atomic orbital and thus, is associated with the term 'subshells.' These subshells are designated by the letters s, p, d, and f, corresponding to l values of 0, 1, 2, and 3, respectively.

Understanding the angular momentum quantum number helps in visualizing the layout of electrons around the nucleus and is fundamental in grasping the complexity of atomic structure. It's like knowing the contours of the land before building a house—the structure's design depends on the terrain it stands on.

Electron Configuration

Now, let's talk about electron configuration, a method of illustrating the arrangement of electrons in an atom's orbitals. Think of electron configuration as the address of an electron, specifying the energy level, subshell, and orbital of each electron. It follows specific rules, such as the Aufbau principle (filling from lower to higher energy levels), Pauli exclusion (no two electrons can have the same set of quantum numbers), and Hund's rule (electrons occupy orbitals singly before pairing).

The electron configuration is essential for understanding the chemical behavior of an atom, as the way electrons are arranged dictates how an atom will react or bond with others. A good grasp of electron configuration can be the difference between understanding why elements react the way they do and merely memorizing their reactions.

Subshell Electron Capacity

Subshell electron capacity refers to the maximum number of electrons that a subshell can accommodate. This number is instrumental when predicting the reactivity and bonding potential of an atom. As we know from our exercise, the s subshell can hold 2 electrons, the p can hold 6, the d can hold 10, and the f can hold 14. This capacity is determined by the formula 2(2l + 1), where 'l' represents the angular momentum quantum number of the subshell.

Knowing the electron capacities of subshells enables us to comprehend the periodicity in the periodic table: why certain groups of elements have similar chemical properties, and why atoms tend toward certain configurations to achieve stability, often resembling the nearest noble gas configuration.