Question

For each of the electron configurations given, write the corresponding orbital diagrams. (a) \(\mathrm{F} \quad 1 s^{2} 2 s^{2} 2 p^{5}\) (b) \(\mathrm{S} \quad 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\) (c) Co \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{7}\) (d) \(\mathrm{Kr} \quad 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{6}\) (e) Ru \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{6} 5 s^{2} 4 d^{6}\)

Short answer

Orbital diagrams are visual representations where each electron is shown as an arrow in a box representing an orbital. For F, show 1s fully occupied, then 2s fully occupied, then 3 out of the 5 available 2p orbitals with one electron each and two with a pair. For S, fully populate 1s through 2p, then 3s, and distribute 4 electrons in the 3p orbitals. Co follows similarly up to 3p, then fill the 4s, and place 7 electrons in the 3d orbitals following Hund's rule. Kr and Ru follow the pattern with completely filled orbitals up to their respective highest occupied sublevels, except for Ru's 4d which receives 6 electrons.

Step-by-step solution

Understand Orbital Diagrams

An orbital diagram is a graphic representation of an electron configuration. It shows each orbital as a box and represents electrons as arrows. The direction of the arrow indicates the electron's spin. Hund's rule states that electrons will occupy empty orbitals before they start pairing up.

Draw Orbital Diagram for F

The electron configuration for fluorine is 1s^2 2s^2 2p^5. Begin with the lowest energy level, the 1s orbital, and fill it with two electrons with opposite spins (indicated by up and down arrows). Then fill the 2s orbital in the same way. Next, draw three p orbitals for the 2p sublevel and distribute five electrons according to Hund's rule.

Sketch Orbital Diagram for S

For sulfur, the electron configuration is 1s^2 2s^2 2p^6 3s^2 3p^4. Follow a similar approach as the previous step, filling the 1s, 2s, and 2p orbitals completely. For the 3s orbital, place two electrons. In the 3p sublevel, distribute four electrons across the three p orbitals following Hund's rule.

Draw Orbital Diagram for Co

Cobalt's electron configuration is 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^7. Fill the 1s, 2s, 2p, 3s, and 3p orbitals completely. Add two electrons to the 4s orbital. Finally, in the 3d sublevel, place seven electrons, ensuring that the first five d orbitals each get one electron before any pairing starts.

Construct Orbital Diagram for Kr

Krypton's electron configuration is 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6. All orbitals from 1s through 4p are completely filled, with each orbital holding the maximum number of electrons and paired spins.

Create Orbital Diagram for Ru

Ruthenium's electron configuration is 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^6. Completely fill the 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and finally two electrons in the 5s orbital. In the 4d sublevel, put one electron in each of the first five orbitals before pairing the sixth electron.

Key concepts

Electron Configurations

Electron configurations are meticulous catalogs of the locations of electrons within an atom's electron shells and subshells, arranged by increasing energy levels.

As an atom grows in size, the complexity of its electron configuration also increases, reflecting the more sophisticated arrangements required to describe the electrons' positions. Understanding an atom's electron configuration is critical because it informs us about an atom’s reactivity, its potential to form bonds with other atoms, and its magnetic characteristics.

To write an electron configuration, you start with the lowest energy level (the 1s orbital), and proceed to fill the orbitals in order following the energies: 1s, 2s, 2p, 3s, and so on. Each orbital can hold a specific maximum number of electrons: two for 's' orbitals, six for 'p' orbitals, ten for 'd' orbitals, and fourteen for 'f' orbitals.

Hund's Rule

Hund's rule gives us insight into how electrons populate an atom's orbitals. It states that electrons will occupy separate orbitals in the same subshell before doubling up.

Think of it like people boarding a bus with plenty of free seats; passengers prefer to sit by themselves before they start sitting next to others. This analogy perfectly mirrors the behavior of electrons, as they fill up orbitals individually before being forced to share space.

Applying Hund's rule while garnishing an orbital diagram ensures that every orbital in the same sublevel gets one electron (with the same spin direction) before any orbital gets a second electron. This is significant because it minimizes electron-electron repulsions and keeps the atom in its most stable, or lowest energy, state.

Electron Spin

The concept of electron spin relates to the intrinsic angular momentum of each electron, which is a fundamental property akin to the electron's charge. Electron spin is quantized, meaning it can only have specific values.

In orbital diagrams, this spin is represented by arrows pointing either up or down. When you see a pair of electrons within an orbital box, one arrow points up and the other down, signifying that the electrons have opposite spins, a requirement according to the Pauli exclusion principle.

The opposite spins allow two electrons to share the same orbital; if they had the same spin, the principle would forbid them from occupying the same quantum state. This knowledge underpins the entire structure of the Periodic Table and the chemical behavior of atoms.