Question

If a \(p\) sublevel has five electrons, which orbitals will they occupy? Draw the sublevel using arrows to represent electrons and show spin based on the direction of the arrow.

Short answer

Electrons occupy all three orbitals singly before pairing; thus, the configuration is: p_x(↑↓), p_y(↑↓), p_z(↑).

Step-by-step solution

Understand the p sublevel

The p sublevel can hold a maximum of 6 electrons and consists of 3 orbitals: p_x, p_y, and p_z.

Distributing the electrons

The five electrons need to be distributed among the three orbitals. According to Hund's rule, electrons will fill all orbitals singly before pairing up, and each electron in a singly filled orbital will have the same spin.

Assign electrons to the orbitals

Place one electron in each of the three orbitals (p_x, p_y, p_z) with the same spin direction (e.g., up). After filling all three orbitals singly, place the remaining two electrons in two of these orbitals with the opposite spin direction (e.g., down).

Draw the p sublevel

Illustrate the distribution as follows:

Key concepts

Hund's rule

In an atom, when electrons occupy orbitals of equal energy (also known as degenerate orbitals), Hund's rule helps determine how they are distributed. According to Hund's rule, electrons will fill each orbital singly before any orbital receives a second electron. Furthermore, all of the single electrons in the degenerate orbitals will have the same spin direction. This means that if you have a set of p orbitals, one electron will go into each orbital (p_x, p_y, p_z) before any orbital gets a second electron.
Hund's rule aims to maximize the total spin, which minimizes electron-electron repulsion and increases stability. For example, in a p sublevel with 5 electrons, you would place one electron in each of the three p orbitals with parallel spins first, and then the remaining two electrons will pair up in any two of the already singly-occupied orbitals, but with opposite spins.

Orbital Diagrams

Orbital diagrams provide a visual way to represent the arrangement of electrons in an atom. Each orbital is usually represented by a box, and arrows within these boxes indicate the electrons. According to the Pauli Exclusion Principle, each box (orbital) can hold a maximum of two electrons with opposite spins.
When constructing an orbital diagram for a p sublevel with five electrons, you would do the following: draw three boxes for the p orbitals (labeled p_x, p_y, and p_z). Place one arrow (representing an electron) with an upward spin in each box. This satisfies Hund's rule. Then, place the remaining two electrons in any two of the boxes, but these arrows must point downward to indicate opposite spin directions.

Electron Spin

Electron spin is a fundamental property of electrons, described by quantum mechanics. Each electron has a spin quantum number, which can be either +1/2 or -1/2. These are conventionally represented by upward (↑) and downward (↓) arrows, respectively.
The concept of electron spin is crucial in understanding how electrons occupy orbitals. According to the Pauli Exclusion Principle, no two electrons in the same orbital can have the same set of quantum numbers. This means that if one electron in an orbital has an upward spin (+1/2), the other must have a downward spin (-1/2).
When dealing with p sublevels, each of the three p orbitals can hold two electrons, one with an upward spin and one with a downward spin. Therefore, for a p sublevel with five electrons, three of the electrons will have the same spin (up) filling each orbital singly, and the remaining two will have the opposite spin (down) pairing up in two of the orbitals.