Question

Designate all the sublevels within each of the following main energy levels: (a) 1 st (b) 2 nd (c) \(3 \mathrm{rd}\) (d) 4 th

Short answer

1st level has 1s; 2nd level has 2s, 2p; 3rd level has 3s, 3p, 3d; 4th level has 4s, 4p, 4d, 4f.

Step-by-step solution

Identify Sublevels for 1st Main Energy Level

The 1st main energy level (also called principal quantum number \(n\)) contains only one sublevel. This sublevel is designated as \(s\). Therefore, the 1st main energy level has one sublevel: \(1s\).

Identify Sublevels for 2nd Main Energy Level

The 2nd main energy level contains two sublevels. These sublevels are designated as \(s\) and \(p\). Therefore, the 2nd main energy level has two sublevels: \(2s\) and \(2p\).

Identify Sublevels for 3rd Main Energy Level

The 3rd main energy level contains three sublevels. These sublevels are designated as \(s\), \(p\), and \(d\). Therefore, the 3rd main energy level has three sublevels: \(3s\), \(3p\), and \(3d\).

Identify Sublevels for 4th Main Energy Level

The 4th main energy level contains four sublevels. These sublevels are designated as \(s\), \(p\), \(d\), and \(f\). Therefore, the 4th main energy level has four sublevels: \(4s\), \(4p\), \(4d\), and \(4f\).

Key concepts

Quantum Numbers

Understanding quantum numbers is crucial for grasping the concept of electron configurations. Quantum numbers are used to describe the properties and locations of electrons within an atom. Think of them like a unique address that helps locate an electron's position in the atom's electron cloud. Here are the four types of quantum numbers:

• Principal Quantum Number ( \(n\) ): It represents the main energy level of an electron. The higher the \(n\) value, the further the electron is from the nucleus of the atom.
• Angular Momentum Quantum Number ( \(l\) ): This number indicates the shape of the electron's sublevel. It can have integer values from 0 to \(n - 1\). For example, if \(n = 2\), \(l\) can be 0 (s sublevel) or 1 (p sublevel).
• Magnetic Quantum Number ( \(m_l\) ): It specifies the orientation of the sublevel's orbital. The range of \(m_l\) values depends on \(l\). For instance, if \(l = 1\), \(m_l\) can be -1, 0, or 1.
• Spin Quantum Number ( \(m_s\) ): This number describes the direction of the electron's spin, either +1/2 or -1/2.

Combining these quantum numbers allows scientists to fully describe the state of an electron in an atom, and helps to predict chemical behavior.

Sublevels

Sublevels are regions within energy levels where electrons are likely to be found. Each main energy level can contain one or more sublevels. The number of sublevels in any given main energy level equals the principal quantum number ( \(n\) ).Here is a breakdown of these sublevels:

• s sublevel: Simple and spherical, the s sublevel can hold up to two electrons and is found in every energy level starting from the first.
• p sublevel: Shaped like dumbbells, p sublevels appear starting from the second energy level and can accommodate up to six electrons.
• d sublevel: This sublevel is more complex, with a double dumbbell shape, appearing from the third energy level onwards. The d sublevel can hold up to ten electrons.
• f sublevel: With an even more intricate shape, the f sublevel can be found starting from the fourth energy level and holds up to fourteen electrons.

Understanding sublevels is key to determining how electrons are distributed in atoms, which in turn helps predict how atoms bond and how molecules form.

Energy Levels

Energy levels are the distinct layers around an atom's nucleus where electrons are likely to reside. Each energy level is associated with a principal quantum number ( \(n\) ) and increases in energy and distance from the nucleus.Here’s a simple breakdown of the main energy levels and their characteristics:

• 1st Energy Level ( \(n = 1\) ): The closest to the nucleus and can hold up to two electrons in a single sublevel (1s).
• 2nd Energy Level ( \(n = 2\) ): Contains s and p sublevels (2s and 2p) holding up to eight electrons combined.
• 3rd Energy Level ( \(n = 3\) ): Has s, p, and d sublevels (3s, 3p, and 3d), accommodating a total of eighteen electrons.
• 4th Energy Level ( \(n = 4\) ): Comprising s, p, d, and f sublevels (4s, 4p, 4d, 4f), it can house up to thirty-two electrons.

These energy levels lay the groundwork for understanding electron distribution within an atom, assisting in predicting atomic structure, behavior, and chemical interactions.