Question

Answer each of the following questions. Be thorough in your answers, and provide complete support. Write the ground-state electron configuration for oxygen. b. Draw the orbital diagram for the ground state of oxygen. Justify your placement of electrons in the diagram. c. Write an electron configuration for oxygen in an excited state. Explain your answer, and show how the orbital diagram would be modified from the one in part b. d. When oxygen returns from an excited state to its ground state, explain why we do not see white light.

Short answer

The ground-state electron configuration for oxygen is \(1s^2 2s^2 2p^4\). The orbital diagram for the ground state is 1s: ↑↓, 2s: ↑↓, 2p: ↑ ↑ ↑, following the Aufbau principle, Pauli exclusion principle, and Hund's rule. In an excited state, electron configuration is \(1s^2 2s^2 2p^3 3s^1\), with a modified orbital diagram showing one electron from the 2p orbital promoted to the 3s orbital. We don't see white light when oxygen returns to its ground state because the energy difference between the 2p and 3s orbitals corresponds to wavelengths outside the visible light range for humans.

Step-by-step solution

Ground State Electron Configuration for Oxygen

Oxygen has an atomic number of 8, which means it has 8 electrons in its neutral atom. Following the Aufbau principle, Pauli exclusion principle, and Hund's rule, we can write the ground state electron configuration for oxygen: \[1s^2 2s^2 2p^4.\]

Draw the Orbital Diagram for Ground State Oxygen

The orbital diagram for the ground state of oxygen is represented as follows: 1s: ↑↓ 2s: ↑↓ 2p: ↑ ↑ ↑ The placement of electrons in the diagram can be justified by the three important rules: - Aufbau Principle: Electrons fill the lowest energy orbitals first. - Pauli Exclusion Principle: Each orbital can hold a maximum of two electrons with opposite spins. - Hund's Rule: Electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible.

Electron Configuration for Oxygen in an Excited State

In an excited state, one or more electrons are promoted to a higher energy orbital. For oxygen, the excited state electron configuration can be written as follows: \[1s^2 2s^2 2p^3 3s^1.\] One electron from the 2p orbital has been promoted to the 3s orbital.

Modify the Orbital Diagram from Part B

The modified orbital diagram for oxygen in an excited state is: 1s: ↑↓ 2s: ↑↓ 2p: ↑ ↑ ↑ 3s: ↑ Here, we see that one of the electrons from the 2p subshell has been excited to the higher energy 3s subshell.

Explain Why We Don't See White Light

When an atom returns from an excited state to its ground state, energy is released in the form of electromagnetic radiation, which can be visible as light. The color of the light depends on the energy difference between the two energy levels the electron is transitioning between. In the case of oxygen, the energy difference between the 2p and 3s orbitals corresponds to wavelengths that are not in the visible light range for human eyes. Therefore, we do not observe white light when oxygen returns from an excited state to its ground state.

Key concepts

Ground-State Electron Configuration

Understanding the ground-state electron configuration of an element is crucial for studying its chemical properties. For the element oxygen, with an atomic number of 8, its ground-state electron configuration is represented as \[1s^{2} 2s^{2} 2p^{4}\]. The configuration denotes that the first two electrons fill the 1s orbital, the next two fill the 2s orbital, and the remaining four are in the 2p orbital.

This particular distribution of electrons is determined by the element's place in the periodic table and can predict its bonding behavior. The configuration also reflects the energy hierarchy of orbitals, indicating which layers of the atom are filled with electrons in its most energetically stable state.

Orbital Diagram

The visual representation of electrons in an atom's orbitals is shown by an orbital diagram. For oxygen, the ground-state orbital diagram is depicted with arrows indicating electron spins:

1s: \[\uparrow\downarrow\]
2s: \[\uparrow\downarrow\]
2p: \[\uparrow\ \uparrow\ \uparrow\]

The paired arrows in the 1s and 2s orbitals indicate two electrons with opposite spins, adhering to the Pauli Exclusion Principle. In the 2p orbitals, each arrow pointing upwards represents an unpaired electron, which follows Hund's rule, maximizing the number of parallel spins within the same subshell.

Excited State Electron Configuration

An atom reaches an excited state when one or more electrons absorb energy and jump to higher energy levels. For oxygen, an excited state electron configuration might look like this: \[1s^{2} 2s^{2} 2p^{3} 3s^{1}\].

This suggests that one electron from the 2p orbital has absorbed enough energy to move to the 3s orbital. Such a transition alters the chemical properties temporarily because the usual pairing and ordering of electrons are disturbed. Excited states are often involved in chemical reactions and the emission of light, which returns the electron to a lower energy state.

Aufbau Principle

The Aufbau principle is vital in determining an element's electron configuration, stating that electrons fill orbitals starting from the lowest energy level moving towards higher levels. 'Aufbau' means 'building up' in German, perfectly encapsulating the concept of gradually filling the orbitals.

With oxygen, the sequence of orbital filling is 1s, followed by 2s, and then 2p, which reflects increasing energy levels. This principle, along with other rules, helps predict and understand the distribution of electrons in the orbitals of an atom.

Pauli Exclusion Principle

One of the fundamentals of quantum mechanics is the Pauli Exclusion Principle, which asserts that no two electrons can have the same set of four quantum numbers in an atom. In simpler terms, it states that an orbital can hold a maximum of two electrons, and they must have opposite spins. This principle explains why the electrons in an orbital diagram for oxygen are paired with one pointing up and the other down in the 1s and 2s orbitals. The presence of this principle ensures the unique placement of electrons within an atom's orbitals.

Hund's Rule

Hund's rule addresses how electrons are distributed among orbitals of the same energy, known as 'degenerate' orbitals. It states that electrons will fill these orbitals singly first, maintaining parallel spins, before any electrons are paired up.

For oxygen, this rule explains the arrangement of the electrons in the 2p orbitals. Despite having space to pair up, each of the 2p orbitals initially contains only one electron to minimize repulsions between electron pairs and to maximize the number of parallel spins, which is energetically favorable. This rule is key to predicting the magnetic properties of an element and the structure of its orbitals.