Problem 66 - Chemistry Matter and Change

Question

How many energy sublevels are contained in each of the hydrogen atom's first three energy levels?

Step-by-Step Solution

Answer

1 sublevel in the first energy level, 2 in the second, and 3 in the third.

Step 1: Understanding Energy Levels

In an atom, electrons occupy energy levels or shells. Each energy level can be subdivided into energy sublevels, which are associated with different types of orbitals (s, p, d, f, etc.). The number of sublevels in a principal energy level is equal to its principal quantum number, denoted by \( n \).

Step 2: Determine Sublevels for First Energy Level

The first energy level (\( n = 1 \)) has only one sublevel because \( n = 1 \). The only sublevel associated with the first energy level is the s-orbital (1s). So, there is 1 sublevel in the first energy level.

Step 3: Determine Sublevels for Second Energy Level

The second energy level (\( n = 2 \)) has two sublevels: s and p. Therefore, there are 2 sublevels in the second energy level (2s and 2p).

Step 4: Determine Sublevels for Third Energy Level

The third energy level (\( n = 3 \)) has three sublevels: s, p, and d. Thus, there are 3 sublevels in the third energy level (3s, 3p, and 3d).

Key Concepts

Orbitals

In the realm of atoms, orbitals are the regions where electrons are most likely to be found. Picture orbitals as the rooms in a hotel, each with its capacity to house electrons. These aren't spatial confines in the classical sense but are defined by the quantum mechanical states that electrons can occupy, known as wave functions.
Each type of orbital has a unique shape and orientation which influences how it interacts with other electrons and atomic structures. For example:

• s-orbitals have a spherical shape, meaning the electron distribution is symmetrical around the nucleus.
• p-orbitals resemble dumbbells, extending in three dimensions which allow them to accommodate more electrons than an s-orbital.
• d-orbitals, with their more complex clover-like shapes, provide even more room for electrons.

The key concept is that each orbital can hold up to two electrons. As we go deeper into each energy level, more orbitals become available to fill with electrons, which contributes to the diverse chemical properties of elements.

Sublevels

The concept of sublevels adds an intricate layer to the understanding of atomic structures by dividing energy levels further into more manageable sections. Each major energy level (also referred to as a shell) is split into sublevels, each corresponding to different types of orbitals.
For instance, the sublevels within any given principal energy level are determined by its principal quantum number, denoted as \( n \).

• For \( n = 1 \), there is only one sublevel: the 1s orbital.
• For \( n = 2 \), there are two sublevels: 2s and 2p.
• For \( n = 3 \), there are three sublevels: 3s, 3p, and 3d.

Each sublevel corresponds to an increasing number of room-like orbitals. This systematic approach not only helps in understanding electron configurations but also in predicting the chemical behavior of elements.

Principal Quantum Number

The principal quantum number, symbolized by \( n \), is integral in defining the primary characteristics of an atom's energy levels. Its value can be any positive integer (1, 2, 3, etc.) and directly impacts the size and energy of the electron’s orbit.
The larger the principal quantum number, the higher the energy level and the larger the atom's corresponding electron orbitals. Here's how it breaks down:

• For \( n = 1 \), the energies are lower, the electron orbitals are smaller, and there is only one sublevel, 1s.
• As \( n \) increases to 2, the energy levels grow, allowing two sublevels: 2s and 2p.
• For \( n = 3 \), we find even more space with three sublevels: 3s, 3p, and 3d.

Thus, \( n \) gives us vital information on the possible distribution of electrons in an atom and is crucial in atomic theory and chemistry.