Problem 56 - Chemistry The Molecular Science

Question

Germanium had not been discovered in the 1870 s when Mendeleev formulated his ideas of chemical periodicity. He predicted its existence, however, and germanium was found in 1886 by Winkler. Write the electron configuration of germanium.

Step-by-Step Solution

Answer

The electron configuration of germanium is \[ \text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \text{4s}^2 \text{3d}^{10} \text{4p}^2 \].

Step 1: Determine the Atomic Number of Germanium

Germanium (Ge) is an element with the atomic number 32. Knowing this helps to determine the number of electrons in a neutral atom of germanium, which is 32 electrons.

Step 2: Understand the Electron Configuration Sequence

To write the electron configuration, it's important to follow the order of filling the atomic orbitals according to the Aufbau principle and Hund's rules. Electrons fill the orbitals in the sequence: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p.

Step 3: Fill Electrons in Order

Start filling the electrons into orbitals as per the sequence until all 32 electrons are placed: - 1s²: 2 electrons - 2s²: 2 electrons - 2p⁶: 6 electrons - 3s²: 2 electrons - 3p⁶: 6 electrons - 4s²: 2 electrons - 3d¹⁰: 10 electrons - 4p²: 2 electrons

Step 4: Write the Electron Configuration

Combine the information from Step 3 into a single sequence that represents the electron configuration of germanium: \[ \text{1s}^2 \text{2s}^2 \text{2p}^6 \text{3s}^2 \text{3p}^6 \text{4s}^2 \text{3d}^{10} \text{4p}^2 \]

Step 5: Verify the Configuration

Ensure that the sum of the superscripts equals the atomic number of germanium (32). This confirms the correct electron configuration: 2 (1s) + 2 (2s) + 6 (2p) + 2 (3s) + 6 (3p) + 2 (4s) + 10 (3d) + 2 (4p) = 32 electrons.

Key Concepts

Atomic Number

Every element in the periodic table is assigned a unique atomic number, which is a fundamental property. The atomic number is the number of protons in an element's nucleus, and in a neutral atom, it is equivalent to the number of electrons. This is what distinguishes one element from another.

For example, germanium has an atomic number of 32. This means that Germanium has 32 protons in its nucleus and, correspondingly, 32 electrons surrounding it. Understanding the atomic number is crucial for determining how electrons are distributed within an atom. It's the starting point for writing an electron configuration, as it tells you how many electrons you need to place within the orbitals of the atom.

In summary, the atomic number gives insight into the atom's structure and is essential for organizing the periodic table. It's like the atom's fingerprint, setting the stage for chemical behavior and properties.

Aufbau Principle

The Aufbau Principle is a fundamental rule in chemistry that helps us determine the electron configuration of an atom. "Aufbau" is a German word that means "building up." This principle states that electrons are added one at a time to the lowest energy orbital available until all electrons are placed.

The order in which orbitals are filled goes from the lowest energy level to the highest. The sequence is:

• 1s
• 2s
• 2p
• 3s
• 3p
• 4s
• 3d
• 4p

When filling the orbitals for germanium, you follow this sequence, ensuring that each level is filled before moving to the next energy level. For instance, the 1s orbital fills before the 2s orbital, which fills before the 2p orbitals, and so on.

The Aufbau principle ensures that the atom's electrons occupy the most stable arrangement possible, minimizing its energy state. This concept is foundational in explaining the structure and behavior of atoms in various chemical reactions.

Hund's Rules

Hund's Rules complement the Aufbau Principle by providing additional guidance on electron placement into orbitals of the same energy. These rules help predict the ground state electron configurations for atoms and their stability.

Hund's Rules can be summarized as follows:

• Every orbital in a sublevel is singly occupied before any orbital is doubly occupied.
• Electrons in singly occupied orbitals all have the same spin to maximize total spin.

When considering the 2p, 3p, or 4p orbitals of germanium as per Aufbau principle, the p orbitals typically have three sub-orbitals. According to Hund's Rules, one electron is placed in each sub-orbital before pairing up. This maximizes parallel spins, which stabilizes the atom.

By following these rules, electrons are distributed in such a way that repulsion between them is minimized, resulting in a more stable and lower energy configuration. This is what helps maintain the chemical identity and behavior of elements in their most stable form.