Orbital diagrams are a foundational concept in chemistry and physics, providing a visual map of where an atom’s electrons reside. This representation shows the distribution of electrons among the various energy levels and sublevels within an atom. The diagram illustrates the location and spin of every electron, offering insight into an atom’s potential chemical behavior and bonding characteristics. Constructing these diagrams is essential for predicting how different elements will interact.
Governing Principles of Electron Filling
The placement of electrons into orbital spaces is governed by three fundamental quantum mechanical rules. The Aufbau principle dictates that electrons must occupy the lowest energy orbitals available before filling higher energy ones. This ensures the atom remains in its most stable, ground state configuration.
The Pauli exclusion principle states that no more than two electrons can share the same orbital space. These two electrons must always possess opposite spins, represented by one arrow pointing up and the other pointing down. This opposing spin is necessary for the two electrons to have unique quantum states.
Hund’s rule applies when multiple orbitals share the same energy level, known as degenerate orbitals. Electrons must first fill these degenerate orbitals singly, with parallel spins, before any pairing begins. For example, each of the three \(p\) orbitals must receive one electron before a second electron is added to any of them, maximizing the number of unpaired electrons.
Mapping Sublevels to Energy Order
Before placing electrons, the orbital diagram’s structure must be established by representing each specific orbital as a box or a short horizontal line. The type of sublevel determines the number of orbitals: \(s\) sublevels have one, \(p\) have three, \(d\) have five, and \(f\) contain seven. Since each orbital holds a maximum of two electrons, these sublevels can hold 2, 6, 10, and 14 electrons, respectively.
The sequence in which these orbitals are arranged is based on their increasing energy, which does not always follow the numerical order of the principal quantum number (\(n\)). The energy ordering begins with \(1s\), followed by \(2s\), \(2p\), \(3s\), and \(3p\). A divergence occurs because the \(4s\) orbital is filled immediately after \(3p\), as the \(4s\) sublevel is slightly lower in energy than the \(3d\) sublevel.
This sequence continues with \(4s\) being filled before \(3d\), and then \(4p\), \(5s\), and so on. This pattern can be determined using a diagonal rule or by referencing the periodic table. The diagram should visually arrange the orbitals vertically, implying that energy increases from the bottom (lowest energy) to the top (highest energy).
Step-by-Step Guide to Constructing Neutral Atom Diagrams
The first step in constructing an orbital diagram for a neutral atom is determining the total number of electrons. This number equals the atomic number. For example, neutral Carbon (C) has an atomic number of 6, meaning it contains 6 electrons to be placed.
Next, set up the energy map starting with the lowest energy orbital, \(1s\). For carbon, the first two electrons fill the \(1s\) orbital. One electron is represented by an upward arrow and the second by a downward arrow to satisfy the Pauli exclusion principle, resulting in the \(1s^2\) configuration.
The third and fourth electrons move to the next-highest energy level, the \(2s\) orbital, and are placed with opposite spins, completing the \(2s^2\) configuration. The remaining two electrons must then be placed into the \(2p\) sublevel, which consists of three degenerate orbitals (\(2p_x\), \(2p_y\), and \(2p_z\)).
Applying Hund’s rule, the fifth electron is placed into the first \(2p\) orbital, and the sixth electron is placed into the second \(2p\) orbital, both with the same spin direction. The third \(2p\) orbital remains empty, as all six electrons have been accounted for. This procedure results in the final orbital diagram for neutral carbon.
Modifying Diagrams for Ions
When creating an orbital diagram for an ion, the initial step involves adjusting the total electron count based on the ion’s charge. For a cation (positively charged), subtract the charge from the atomic number. For an anion (negatively charged), add the charge magnitude to the atomic number. Anions simply place the newly acquired electrons into the next available orbital following the standard filling rules.
The electron removal process for cations is more nuanced, especially for transition metals. Electrons are always removed from the shell with the highest principal quantum number (\(n\)) first. For example, in a \(4s^23d^x\) configuration, the two electrons are removed from the \(4s\) orbital before any are removed from the \(3d\) orbitals.
Although \(4s\) fills before \(3d\) in the neutral atom, the \(4s\) orbital is spatially further from the nucleus and has a higher energy level in the resulting ion. This means the outermost \(4s\) electrons are less tightly bound than the \(3d\) electrons once the atom is ionized. For instance, drawing the diagram for \(\text{Fe}^{2+}\) (starting with \(4s^23d^6\)) requires removing the two electrons from the \(4s\) orbital first. The resulting diagram shows an empty \(4s\) orbital and a filled \(3d\) sublevel.