Question

Why do the two electrons in the $2p$ sublevel of carbon occupy different $2p$ orbitals?

Short answer

The two electrons in the 2p sublevel of carbon occupy different 2p orbitals because of Hund's rule and the Pauli exclusion principle. Hund's rule states that electrons will occupy orbitals singly before pairing up, minimizing electron repulsion. The Pauli exclusion principle ensures that two electrons in the same orbital must have opposite spins. Thus, the two electrons in the 2p sublevel fill into separate orbitals (2px and 2py) with parallel spins, minimizing repulsion while adhering to these principles.

Step-by-step solution

Electron Configuration of Carbon

Carbon has an atomic number of 6, meaning it has 6 electrons. Its electron configuration is 1s² 2s² 2p². This means that carbon has 2 electrons in the 1s shell, 2 electrons in the 2s shell, and 2 electrons in the 2p subshell.

Orbitals in 2p Sublevel

In the 2p sublevel, there are three orbitals which are 2px, 2py, and 2pz orbitals. Each of these orbitals is at the same energy level and can hold a maximum of 2 electrons.

Aufbau Principle and Hund's Rule

The Aufbau principle states that electrons fill the orbitals in order of increasing energy. On the other hand, Hund's rule states that when there are multiple orbitals with the same energy level, such as the 2p sublevel, electrons will occupy the orbitals singly before pairing up. That is because electrons have a repulsion force between them due to their negative charge.

Electron Spin

Electrons have two possible spin states, denoted as “spin up” and “spin down.” In order to occupy the same orbital, two electrons must have opposite spins according to the Pauli exclusion principle.

Putting It All Together

For carbon, in the 2p sublevel, there are two electrons to fill into the 2px, 2py, or 2pz orbitals, which are at the same energy level. Following Hund's rule, these electrons will occupy separate 2p orbitals (2px and 2py) before considering to double up, with parallel spins (either both spin up or both spin down). Therefore, the two electrons in the 2p sublevel of carbon occupy different 2p orbitals according to Hund's rule and Pauli's exclusion principle, ensuring their spins are parallel while minimizing electron repulsion.

Key concepts

Orbitals

Orbitals are regions in an atom where there is a high probability of finding electrons. These are defined based on the energy level and shape. For each principal energy level (n), there are different types of orbitals like s, p, d, and f.

• s-orbitals: Spherical in shape and can hold a maximum of 2 electrons.
• p-orbitals: Shaped like dumbbells and consist of three different orientations designated as 2px, 2py, and 2pz. Each can hold up to 2 electrons.

In any atom, electrons fill these orbitals based on their energy levels. This process inherently affects how chemical bonding and reactions occur. Orbitals provide a fundamental framework for understanding how electrons distribute themselves in an atom and interact with each other.

Hund's Rule

Hund's Rule is vital for determining how electrons are distributed across orbitals of the same energy level or subshell. This rule states that electrons will fill orbitals singly before any orbital gets a second electron.

• This is done to minimize electron-electron repulsion, as electrons are negatively charged and repel each other.
• When electrons are added to degenerate orbitals (orbitals with the same energy level), they prefer to have parallel spins in separate orbitals until each one has at least one electron.

For carbon's 2p sublevel, Hund's Rule explains why electrons occupy the 2px and 2py orbitals separately, before pairing up. This distribution maximizes spin multiplicity, which is favorable in terms of energy.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a foundational theory in quantum mechanics that directly affects electron configurations. It posits that no two electrons can have the same set of quantum numbers in an atom. Each electron in an atom must be unique in terms of its quantum state.

• As a result, no two electrons in the same orbital can have the same spin. Typically, one is 'spin up' and the other is 'spin down.'
• This principle ensures that electrons are spread out and accounts for certain limitations in electron configuration.

In the context of carbon's 2p sublevel, while Hund's Rule explains the distribution of electron spins, the Pauli Exclusion Principle clarifies why spins must be opposite when two electrons finally share the same orbital.

Aufbau Principle

The Aufbau Principle is a guideline for the order in which orbitals are filled by electrons. It helps predict the electron configuration of atoms from hydrogen onward.

• Electrons occupy the lowest energy orbitals available before filling higher energy ones. This is why electrons fill 1s before 2s, 2s before 2p, and so forth.
• The principle reflects a fundamental pattern observed in the organization of the periodic table, explaining the filling sequence.

This principle provides the basis for deriving the electron configuration of any element, including carbon. According to the Aufbau Principle and the sequential filling of orbitals, carbon's configuration ends with electrons entering the 2p orbitals, adhering to this principle's ascending energy criteria.