Question

What is the maximum number of electrons that can fill a \(2 p\) sublevel?

Short answer

The maximum number of electrons that a 2p sublevel can hold is 6.

Step-by-step solution

Understand Quantum Numbers

Each atomic orbital is described by a set of quantum numbers: n, l, m and s. 'n' is the principle quantum number, 'l' is the azimuthal quantum number, 'm' is the magnetic quantum number and 's' is the spin quantum number. The 'n' quantum number denotes the energy level, in this case it is 2, so we are looking at the 2nd energy level. The 'l' quantum number denotes the sublevel (s, p, d or f), in our case it is 'p'.

Calculate Orbitals

For a p sublevel, the 'l' value is 1. The 'm' quantum number which denotes the number of orbitals can have values from -l to +l. This means that in a p sublevel, 'm' can be -1, 0 or 1. So, there are 3 orbitals in a p sublevel.

Calculate Electron Capacity

Each orbital can hold a maximum of 2 electrons, this is given by the Pauli Exclusion Principle. Each electron in an orbital has a distinct spin quantum number (denoted by 's'), which can be either +1/2 or -1/2. Since there are 3 orbitals in a p sublevel, to calculate the maximum electron capacity, multiply the number of orbitals by the maximum electron capacity of each orbital. This gives \( 3 \times 2 = 6 \) electrons.

Key concepts

Atomic Orbital

Atomic orbitals are regions in an atom where there is a significant probability of finding an electron. These orbitals have different shapes and sizes, and they help us understand where electrons are located around an atom's nucleus. The concept of orbitals is fundamental to quantum chemistry and it plays a crucial role in defining the electronic structure of atoms.

There are different types of orbitals, namely s, p, d, and f. Each type has its unique shape:

• s orbital: Spherical shape, usually found at the base energy levels.
• p orbital: Dumbbell shape, consists of three orbitals aligned along the x, y, and z axes.

Each of these orbitals is described using quantum numbers. For a 2p sublevel, the important quantum number **l** equals 1, leading to three orientations or magnetic quantum numbers, -1, 0, and +1, accounting for the three orbitals in a p sublevel.

Understanding atomic orbitals helps us predict how atoms bond and interact with each other, and is key to understanding chemistry at a fundamental level.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a fundamental rule in quantum mechanics concerning electron configurations within atomic orbitals. It states that no two electrons in the same atom can have the same set of quantum numbers. In simple terms, no two electrons can occupy the same exact space in an atom.

Here's how it works in the context of orbitals:

• Each orbital can hold up to two electrons.
• These electrons must have opposite spins, represented by the spin quantum numbers +1/2 and -1/2.

When applied to a p sublevel, like the 2p sublevel discussed earlier, the principle dictates that each of the three orbitals in this sublevel can have two electrons, making a total of six electrons for this entire sublevel.

The Pauli Exclusion Principle is crucial for understanding the behavior of electrons in atoms and the formation of chemical bonds.

Electron Capacity

Electron capacity refers to the maximum number of electrons an atomic orbital or a set of orbitals can hold. Determining the electron capacity of orbitals is essential for understanding the arrangement of electrons around an atom, which is foundational for the study of chemical reactions and bonding.

As you've seen for the 2p sublevel:

• There are three orbitals available in a p sublevel.
• Each orbital can accommodate up to two electrons.

To calculate the electron capacity of the 2p sublevel, multiply the number of orbitals (3) by the number of electrons each can hold (2), resulting in 6 electrons.

This concept not only helps predict how atoms interact but also explains elements' positions in the periodic table, influencing an element's properties and reactivity.