Question

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

Short answer

The number of sublevels is equal to the principal quantum number \(n\): 1st has 1, 2nd has 2, 3rd has 3, 4th has 4.

Step-by-step solution

Understand the Quantum Level Structure

Each main energy level, or principal quantum number, is denoted by the letter \(n\). It indicates the energy level occupied by an electron in an atom. The number of sublevels within a given principal energy level \(n\) is equal to \(n\).

Determine Sublevels for 1st Energy Level

For the 1st main energy level (\(n = 1\)), there is 1 sublevel. This is the \(s\) sublevel.

Determine Sublevels for 2nd Energy Level

For the 2nd main energy level (\(n = 2\)), there are 2 sublevels: \(s\) and \(p\) sublevels.

Determine Sublevels for 3rd Energy Level

For the 3rd main energy level (\(n = 3\)), there are 3 sublevels: \(s\), \(p\), and \(d\) sublevels.

Determine Sublevels for 4th Energy Level

For the 4th main energy level (\(n = 4\)), there are 4 sublevels: \(s\), \(p\), \(d\), and \(f\) sublevels.

Key concepts

Principal Quantum Number

The principal quantum number, denoted by the symbol \( n \), is a fundamental concept in quantum mechanics. It represents the main energy level or shell where an electron resides within an atom. Each increase in the principal quantum number corresponds to a higher energy level and a greater distance from the nucleus.
The principal quantum number is always a positive integer (\( n = 1, 2, 3, \) etc.). For example:

• For \( n = 1 \), the electron is in the first main energy level.
• For \( n = 2 \), the electron is in the second main energy level, and so on.

The higher the value of \( n \), the more sublevels and orbitals an energy level contains. This quantum number is essential to understand the electron configuration and distribution within an atom.

Electron Configuration

The term 'electron configuration' describes how electrons are distributed within the orbitals of an atom. It is fundamentally determined by the principal quantum number \( n \) and the sublevel types (like \( s \), \( p \), \( d \), and \( f \)).
Each energy level with a specific \( n \) can hold a certain number of electrons:

• The first energy level (\( n = 1 \)) has only an \( s \) sublevel.
• The second level (\( n = 2 \)) adds a \( p \) sublevel.
• The third level (\( n = 3 \)) includes \( s \), \( p \), and \( d \) sublevels.
• The fourth level (\( n = 4 \)) includes \( s \), \( p \), \( d \), and \( f \) sublevels.

This configuration helps determine where electrons reside and how they interact with each other and external elements. Electron configurations dictate chemical properties, reactivity, and bonding behavior.

Energy Levels

Energy levels refer to the specific regions within an atom where electrons are likely to be found. These levels are dictated by the principal quantum number \( n \), with each level possessing sublevels (\( s \), \( p \), \( d \), \( f \)). These sublevels have different energies and shapes.
The lowest energy level is closest to the nucleus, and as the number \( n \) increases, the energy levels become higher and spaced further away:

• Level 1 has only the \( s \) sublevel.
• Level 2 includes \( s \) and \( p \) sublevels.
• Level 3 adds \( d \) to the mix.
• By level 4, the \( f \) sublevel is also present.

Each main energy level can hold a specific number of electrons, calculated as \( 2n^2 \). Understanding these levels is crucial for predicting electron arrangement and chemical behavior.

Atomic Structure

Atomic structure comprises protons, neutrons, and electrons. The nucleus contains protons and neutrons, while electrons orbit around the nucleus within specific energy levels marked by the principal quantum number \( n \).
These levels are further subdivided into sublevels or orbitals, which define an electron's possible locations. The structure and arrangement of these sublevels influence an atom's properties:

• Protons and neutrons provide the atomic nucleus its mass and identity.
• Electrons occupy orbitals in increasing energy levels, starting from the lowest levels.
• Atoms seek stability through fully occupied sublevels, frequently engaging in reactions to achieve such configurations.

Understanding atomic structure with its intricate arrangement and interaction between particles aids in comprehending chemical bonding and periodic properties.