Question

Which of the following electron configurations \((\mathrm{a}-\mathrm{f})\) are for atoms in the ground state? In the excited state? Which are impossible? (a) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 3 \mathrm{~s}^{2}\) (b) \(1 \mathrm{~s}^{2} 2 \mathrm{p}^{3}\) (c) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{3} 2 \mathrm{p}^{5}\) (d) \(1 s^{2} 2 s^{2} 2 p^{7}\) (e) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 2 \mathrm{p}^{6} 3 \mathrm{~s}^{1}\) (f) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 2 \mathrm{p}^{6} 3 \mathrm{~s}^{2} 3 \mathrm{~d}^{1}\)

Short answer

Question: Classify each given electron configuration as either ground state, excited state, or impossible. Answer: Configurations (a), (b), and (e) are in the ground state, configuration (f) is in the excited state, and configurations (c) and (d) are impossible.

Step-by-step solution

Analyze Electron Configurations (a) - (c)

For (a), the configuration obeys all mentioned principles. Thus, it's a ground state configuration. For (b), it also follows the principles and represents a ground state. For (c), we can see that there are 3 electrons in the 2s orbital, which violates the Pauli Exclusion Principle (maximum 2 electrons per orbital), thus making this configuration impossible.

Analyze Electron Configurations (d) - (f)

For (d), having 7 electrons in the 2p orbital violates the Pauli Exclusion Principle since there's a maximum of 6 electrons allowed (2 per each of the 3 degenerate orbitals). Thus, this configuration is impossible. For (e), this obeys all the mentioned principles, and it's a ground state configuration. For (f), all the rules are followed, but because the 3d orbital is filled before the 3p, which doesn't follow the Aufbau Principle's order, this configuration represents an excited state.

Write the final answer

With the evaluation of each electron configuration, it can be concluded that: - Configurations (a), (b), and (e) are in the ground state. - Configuration (f) is in the excited state. - Configurations (c) and (d) are impossible.

Key concepts

Ground State

The ground state of an atom is the lowest energy configuration of its electrons. When we talk about the ground state, we refer to the arrangement of electrons around the nucleus where they occupy the lowest available energy levels according to established rules.

Like a ladder, electrons fill up the 'rungs' or energy levels starting from the bottom. First, they fill the 1s orbital, then the 2s, and so on in a predictable pattern described by the Aufbau Principle. An electron in the ground state would not occupy a higher energy orbital (like 3d) if there are still empty or partially filled lower energy orbitals (like 3p) available. In the given exercise, configurations (a), (b), and (e) depict electrons in their ground state because they adhere to the natural order of electron filling without violating any rules.

Excited State

The excited state occurs when an electron within an atom absorbs energy and jumps to a higher energy level that is not the most stable configuration. Electrons generally occupy the lowest energy orbitals they can due to the rules of nature, but when given extra energy, they can move to higher levels, even if temporarily.

This excited configuration is less stable, and the electron will eventually release energy to fall back down to the ground state. In our exercise, configuration (f) is an example of an atom in an excited state because it has an electron in the 3d orbital before the 3p orbital is filled, which deviates from the normal 'ground state' electron filling order.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a fundamental rule in quantum mechanics, stating that no two electrons in an atom can have identical quantum numbers. In essence, an orbital can hold a maximum of two electrons, and they must have opposite spins.

When applying this principle to electron configurations, it explains why certain configurations are impossible. Configurations (c) and (d), as identified in the exercise solution, violate this principle since they have an excess number of electrons within a single orbital (3 electrons in the 2s orbital and 7 electrons in the 2p orbital, respectively). This overpopulation of orbitals is not possible according to the Pauli Exclusion Principle, making these configurations impossible.

Aufbau Principle

The Aufbau Principle helps us predict the electron configurations of atoms by showing us how electrons fill up orbitals. Derived from a German word meaning 'building up', this principle states that electron orbitals fill with electrons in order of increasing energy level, starting with the lowest energy orbital.

Electrons are added one by one to the lowest energy orbitals before moving to higher energy orbitals. However, due to certain rules about orbital shapes and how they fill, sometimes this filling order can seem less intuitive, such as when filling the d and f orbitals. According to the Aufbau Principle, the correct order of electron filling would go from 1s to 2s to 2p to 3s, and so on. In our exercise, configuration (f) goes against the expected order by filling a 3d orbital prior to filling 3p orbitals, indicating an atom in an excited state.