Problem 7 - Chemistry in 30 days

Question

Any p-orbital can accommodate up to: (a) 4 electrons (b) 2 electrons with parallel spins (c) 6 electrons (d) 2 electrons with opposite spins

Step-by-Step Solution

Answer

(c) A p-orbital can accommodate up to 6 electrons.

Step 1: Understanding Electron Accommodation

Electron accommodation refers to the ability of an orbital to hold electrons. Each orbital can hold a maximum number of electrons and for specific orbitals, this capacity is fixed.

Step 2: Identifying Electron Capacity of a p-orbital

A p-orbital is a type of atomic orbital that can contain electrons. The p-orbital can actually hold up to 6 electrons.

Step 3: Analyzing Electron Spin

Electrons in orbitals are also characterized by their spin, which can be either 'up' (↑) or 'down' (↓). According to Pauli's Exclusion Principle, an orbital can accommodate electrons with opposite spins.

Step 4: Evaluating Each Option

(a) 4 electrons - Incorrect, a p-orbital can hold 6 electrons. (b) 2 electrons with parallel spins - Incorrect, two electrons in the same orbital must have opposite spins. (c) 6 electrons - Correct, this is the electron capacity of a p-orbital. (d) 2 electrons with opposite spins - Correct for a single available p-orbital, but a whole p subshell can hold 6 electrons.

Key Concepts

Electron Accommodation in Orbitals

Electron accommodation refers to how many electrons an orbital can hold. This is a fundamental concept in understanding how electrons are distributed in an atom. Each type of orbital—whether it's an s, p, d, or f orbital—can hold a specific maximum number of electrons. This capacity is determined by the quantum mechanical properties of electrons. For instance, the p-orbital we are concerned with can accommodate up to 6 electrons. This is because a p subshell consists of three individual p-orbitals (each can hold 2 electrons), collectively totaling up to 6 electrons. When talking about electron accommodation, it is crucial to understand the structure of the atom and the distribution of different orbitals around the nucleus. atoms arrange their electrons in these orbitals to maintain stability and minimize energy.

Pauli's Exclusion Principle

Pauli's Exclusion Principle is a key rule in quantum mechanics. It states that no two electrons in an atom can have the same set of four quantum numbers. This principle helps explain why each orbital can hold a maximum of two electrons with opposite spins. When electrons are filling an orbital, they must pair up with opposite spins, like ⬆️ and ⬇️. This ensures that their quantum states are distinct.

• Both electrons in an orbital must have different spins to not violate Pauli's principle.
• It effectively imposes a restriction on electron configuration, ensuring uniqueness in how electrons fill up orbitals.

This principle is crucial when predicting and understanding the electronic structure of atoms, affecting their chemical properties and bonding.

Understanding Electron Spin

Electrons have a property known as "spin," which can be thought of as a rotation around their own axis. While this is more of a quantum property than a physical spinning motion, it is described as if an electron is spinning either "up" or "down." Electron spin is represented with arrows:

• ⬆️ for "up" spin
• ⬇️ for "down" spin

In any given orbital, electrons pair with opposite spins due to Pauli's Exclusion Principle. This is crucial because it allows orbitals to be filled in a way that adheres to quantum mechanical principles. The concept of electron spin also leads to the designation of an electron's magnetic properties. It is essential when considering atomic interactions and chemical bonding.

Atomic Orbital Capacity

The concept of atomic orbital capacity is fundamental when learning about atomic structure. Each type of atomic orbital has a specific capacity:

• s-orbitals can hold 2 electrons.
• p-orbitals can accommodate up to 6 electrons.
• d-orbitals can contain up to 10 electrons.
• f-orbitals have a capacity of 14 electrons.

This capacity determines how atoms fill their outer shells and thus predicts their stability and reactivity. In a p-orbital, all three (px, py, pz) can each hold 2 electrons, meaning collectively, a p subshell can hold 6 electrons. These capacities arise from the need to fill each orbital with electron pairs, as dictated by Hund's rule and quantum mechanics, providing a complete picture of electron distribution in atoms.