Question

a. In your own words, state the Aufbau principle. b. Explain the meaning of this principle in terms of an atom with many electrons.

Short answer

Electrons occupy lowest energy orbitals first (Aufbau principle). In many-electron atoms, this principle guides the electron configuration from lowest to higher energy orbitals sequentially.

Step-by-step solution

State the Principle

The Aufbau principle explains how electrons fill atomic orbitals. It states that electrons occupy the lowest energy orbitals first before filling higher energy orbitals.

Interpret the Principle for Many-Electron Atoms

For an atom with many electrons, the Aufbau principle means that electrons will fill orbitals in an energy sequence starting from the lowest available. This helps in predicting electron configurations. Therefore, the sequence begins with 1s, followed by 2s, 2p, 3s, and so on.

Key concepts

Electron Configuration

Electron configuration refers to the arrangement of electrons in an atom’s atomic orbitals. This configuration helps determine the chemical properties of an element. Electrons occupy orbitals based on their energy levels, following specific rules like the Aufbau principle, Hund’s rule, and Pauli exclusion principle.

ELECTRON DISTRIBUTION RULES

1. The Aufbau principle dictates that electrons fill lower energy orbitals first.
2. Hund’s rule states that electrons will fill degenerate orbitals (orbitals of the same energy) singly before pairing up.
3. The Pauli exclusion principle asserts that no two electrons can have the same set of quantum numbers within an atom.

The standard notation for electron configuration uses the principal quantum number (n) and the letter representing the sublevel (s, p, d, f) followed by a superscript denoting the number of electrons in those orbitals. For example, the electron configuration of carbon (atomic number 6) is written as 1s² 2s² 2p².

Atomic Orbitals

Atomic orbitals are regions within an atom where electrons are most likely to be found. These orbitals are described by quantum numbers and come in different shapes (s, p, d, f) corresponding to different energy levels. The 's' orbitals are spherical, 'p' orbitals are dumbbell-shaped, 'd' orbitals are clover-shaped, and 'f' orbitals have more complex shapes.

ORBITAL TYPES AND SHAPES

1. 's' orbitals have a spherical shape and can hold a maximum of 2 electrons.
2. 'p' orbitals have a dumbbell shape and can hold up to 6 electrons.
3. 'd' orbitals have a clover shape and can accommodate up to 10 electrons.
4. 'f' orbitals are even more complex, holding up to 14 electrons.

The probability density function of these orbitals provides a visual representation of where an electron is likely to be found. As electrons fill these orbitals, they follow guidelines set by principles like the Aufbau principle in order to achieve the lowest energy and most stable configuration.

Energy Levels

Energy levels, also known as electron shells, are the fixed distances from the nucleus of an atom where electrons may reside. These levels are denoted by principal quantum numbers (n = 1, 2, 3, ...).

HIERARCHY OF ENERGY LEVELS

1. The first energy level (n=1) can hold up to 2 electrons in a single 's' orbital.
2. The second energy level (n=2) consists of 1 's' orbital and 3 'p' orbitals, holding up to 8 electrons.
3. The third energy level (n=3) includes 1 's' orbital, 3 'p' orbitals, and 5 'd' orbitals, accommodating up to 18 electrons.
4. Higher energy levels (n=4 and above) include additional 'f' orbitals, with even more complex structures.

Energy levels increase in energy as they move farther from the nucleus. According to the Aufbau principle, electrons fill the lowest available energy levels first before moving to higher ones. This arrangement minimizes the atom’s energy, creating a stable structure.