Question

Write the full ground-state electron configuration for each: (a) \(\mathrm{Rb}\) (b) Ge (c) Ar

Short answer

(a) \(\text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \text{4s}^2 \text{3d}^{10} \text{4p}^6 \text{5s}^1\). (b) \(\text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \text{4s}^2 \text{3d}^{10} \text{4p}^2\). (c) \(\text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6\).

Step-by-step solution

- Identify Atomic Numbers

Determine the atomic number (number of protons) for each element. (a) \(\text{Rb}\): atomic number is 37. (b) \(\text{Ge}\): atomic number is 32. (c) \(\text{Ar}\): atomic number is 18.

- Use the Aufbau Principle

Apply the Aufbau Principle to fill in the electron configurations from lower to higher energy levels.(a) \(\text{Rb}\): electrons fill up in the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s for atomic number 37.(b) \(\text{Ge}\): electrons fill up in the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p for atomic number 32.(c) \(\text{Ar}\): electrons fill up in the order 1s, 2s, 2p, 3s, 3p for atomic number 18.

- Write the Full Electron Configuration

Combine the filled orbitals for each element.(a) \(\text{Rb}\): \(\text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \text{4s}^2 \text{3d}^{10} \text{4p}^6 \text{5s}^1\).(b) \(\text{Ge}\): \(\text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \text{4s}^2 \text{3d}^{10} \text{4p}^2\).(c) \(\text{Ar}\): \(\text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6\).

Key concepts

Aufbau Principle

Understanding the Aufbau Principle helps us determine the electron configuration for atoms. It states that electrons fill atomic orbitals in order of increasing energy levels. This means electrons fill the lowest energy orbitals first before moving to higher ones. For example, before filling the 2s orbital, we must fill the 1s orbital.

Also, each following orbital type (s, p, d, f) has a specific order based on its energy.

• s orbitals fill first
• then p orbitals
• then d orbitals
• and finally, f orbitals

The principle also takes into account the Pauli Exclusion Principle, which states that an orbital can hold a maximum of two electrons with opposite spins.

By following this principle, you can write the electron configurations for elements accurately. For example, the configuration of Rubidium (Rb) is determined by moving from the 1s orbital up to the 5s orbital in the order of increasing energy.

Atomic Number

The atomic number is a fundamental property of an element that indicates the number of protons in the nucleus of an atom. Each element has a unique atomic number, which determines its position on the periodic table. Since atoms are neutral, the atomic number also equals the number of electrons in a neutral atom.

For instance, the elements in your exercise have the following atomic numbers:

• Rubidium (Rb): Atomic number 37
• Germanium (Ge): Atomic number 32
• Argon (Ar): Atomic number 18

Knowing the atomic number is essential when writing the electron configuration as it tells you the total number of electrons you are to distribute across the orbitals according to the Aufbau Principle.

Electron Configuration

An electron configuration describes the distribution of electrons across the orbitals of an atom. By knowing the electron configuration, you can understand an element’s chemical properties and its position in the periodic table.

The general format for writing electron configurations is to list each occupied orbital and the number of electrons in those orbitals. Here is how we write the electron configurations for the given elements:

(a) **Rubidium (Rb), Atomic Number 37:**
Configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1\)
Rubidium's electrons fill from the 1s orbital up to the 5s orbital.

(b) **Germanium (Ge), Atomic Number 32:**
Configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^2\)
Germanium's electrons fill up to the 4p orbital.

(c) **Argon (Ar), Atomic Number 18:**
Configuration: \(1s^2 2s^2 2p^6 3s^2 3p^6\)
Argon's electrons fill up to the 3p orbital.

Understanding these electron configurations is vital because they explain the placement of electrons in atomic orbitals, which in turn determines the reactivity and chemical behavior of the element.