Question

Draw a filling diagram and predict the sublevel that follows \(4 s\).

Short answer

The sublevel that follows 4s is 3d.

Step-by-step solution

Understand the Electron Configuration Order

The electron configuration of atoms follows a specific order known as the Aufbau principle. This principle states that electrons occupy the lowest energy sublevel available. The order of filling is generally given by the sequence of sublevels: 1s, 2s, 2p, 3s, 3p, 4s, and so on.

Draw the Energy Level Diagram

Begin by drawing an energy level diagram that stacks sublevels in their order of increasing energy. For visual clarity, write each sublevel in a diagonal slant starting from 1s, ending with higher levels. The sublevels should be drawn as follows: - 1s - 2s - 2p - 3s - 3p - 4s Note how 3d will appear after 4s as per the energy level filling rule.

Applying the (n+l) Rule

Apply the (n+l) rule where n is the principal quantum number, and l is the azimuthal quantum number (s=0, p=1, d=2, f=3). The sublevels are filled in order of increasing (n+l) values. If two sublevels have the same (n+l) value, the sublevel with the lower principal quantum number (n) is filled first.

Identify the Sublevel After 4s

Using the energy level diagram and (n+l) rule, determine that after 4s, the next sublevel is 3d, because for 4s, n=4, l=0, and n+l = 4. For 3d, n=3, l=2, and n+l = 5, which comes right after the n+l = 4 of 4s.

Key concepts

Aufbau Principle

The Aufbau Principle is a key guideline for determining the electron configuration of an atom. It proposes that electrons fill orbitals starting with the lowest energy levels and then proceed to higher ones. This principle is essential to understand because it allows us to predict how electrons are distributed in an atom, which in turn influences an atom's chemical properties. The sequence generally follows a pattern such as: 1s, 2s, 2p, 3s, 3p, 4s, and then continuing as needed. This is known as the Aufbau order.
The word 'Aufbau' means 'building up' in German, highlighting how electrons build up in an atom sequentially in energy levels. Deviations from this principle may occur due to electron-electron interactions at higher levels, but it serves as a fundamental rule for constructing ground-state electron configurations.

Energy Level Diagram

An energy level diagram visually represents the order in which atomic sublevels are filled according to their energy. This helpful tool stacks up sublevels starting with the lowest energy, which is 1s, and then progresses upward to higher energies like 2s, 2p, and continues onward. In the diagram, the levels are often written in a diagonal slant.

• **1s**: Lowest energy level with one orbital.
• **2s and 2p**: Comes next, with 2s before 2p due to lower energy.
• **3s and 3p**: Fills following 2p; 3s before 3p.
• **4s**: This level fills before 3d despite numerically being 4, due to its lower energy state.

After 4s is filled, electrons proceed to the higher energy 3d sublevel. Each sublevel is characterized by its shape and the number of orbitals it contains, contributing to the establishment of the full electron configuration for atoms.

Quantum Numbers

Quantum numbers are crucial for describing the specific properties of electrons within an atom, essentially acting like an address. The four quantum numbers are:

• **Principal Quantum Number (n)**: Indicates the main energy level. It determines the shell and can be any positive integer. For example, 3s has a principal quantum number of n=3.
• **Azimuthal Quantum Number (l)**: Indicates the subshell or shape of the orbital. It can range from 0 to (n-1). For instance, s (l=0), p (l=1), d (l=2), and f (l=3).
• **Magnetic Quantum Number (m_l)**: Specifies the exact orbital within a subshell, and ranges from -l to +l.
• **Spin Quantum Number (m_s)**: Denotes the spin of the electron, either +1/2 or -1/2, showing the two possible states of an electron's spin.

These numbers work together to provide a specific framework of where an electron resides in an atom, giving a greater understanding and prediction capability concerning the electron configuration and positioning.