Question

For each of the electron configuration given, write the corresponding orbital diagrams. (a) \(\mathrm{Cl} \quad 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5}\) (b) \(\mathrm{Mg} \quad 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\) (c) \(\mathrm{Ni} \quad 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{8}\) (d) \(\mathrm{Cu} \quad 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{9}\) (e) Ba \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{6} 5 s^{2} 4 d^{10} 5 p^{6} 6 s^{2}\)

Short answer

Cl: Arrow diagram with 2 arrows in 1s, 2s, 2p, and 3s orbitals; 3p orbital with 5 arrows; Mg: 2 arrows in each of 1s, 2s, 2p, and 3s orbitals; Ni: 2 arrows in 1s, 2s, 2p, 3s, and 4s orbitals, 3p with 6 arrows, and 3d with 8 arrows; Cu: 2 arrows in 1s, 2s, 2p, 3s, and 4s orbitals, 3p with 6 arrows, 3d with 9 arrows; Ba: 2 arrows in each of 1s, 2s, 2p, 3s, 4s, 3d, 4p, 5s, and 4d orbitals, 5p with 6 arrows, 6s with 2 arrows.

Step-by-step solution

- Understanding Electron Configurations and Orbital Diagrams

Electron configurations indicate the arrangement of electrons around a nucleus. An orbital diagram represents this arrangement with boxes or lines for each orbital and arrows for electrons. The electrons fill up in the order of increasing energy levels (1s, 2s, 2p, etc.) following Hund's rule (which states that electrons will occupy empty orbitals in the same subshell before pairing up) and the Pauli exclusion principle (each orbital can hold a maximum of two electrons with opposite spins).

- Draw Orbital Diagram for Chlorine (Cl)

Follow the electron configuration for Cl (1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{5}) and represent each orbital with a box and each electron with an arrow. Fill each orbital with at most two electrons with opposite spins. In the 3p subshell, distribute five electrons in three boxes, respecting Hund's rule.

- Draw Orbital Diagram for Magnesium (Mg)

The electron configuration for Mg is 1s^{2} 2s^{2} 2p^{6} 3s^{2}. Draw boxes for each orbital, filling up the lower energy orbitals first. The last orbital (3s) will have two electrons with opposite spins.

Key concepts

Electron Configurations

Understanding the layout of electrons within an atom is crucial in chemistry, and electron configurations serve as a roadmap for this purpose. They tell us how electrons are distributed among the orbitals of an atom. Represented by a series of numbers and letters, such as 1s² or 2p⁶, these configurations follow a specific order based on the increasing energy levels of orbitals.

Electrons fill up the lowest energy orbitals first, which is a statement of the Aufbau principle. For example, the first electrons an atom receives will occupy the 1s orbital, moving on to the 2s and 2p orbitals as more electrons are added. This sequence continues in an established pattern known as the sequence of orbital filling, taking into account the various sublevels within each principal energy level.

It's essential for students to visualize orbital diagrams while learning electron configurations. These diagrams augment the configurations by showing individual orbitals as boxes (or lines) and electrons as arrows. The arrows are drawn pointing upward or downward representing electron spins. Such visualization aids in comprehending the arrangement of the subatomic particles in an atom and the principles that govern this arrangement.

Hund's Rule

While filling up orbitals with electrons, it's not just about who comes first; there are rules of 'sharing space.' This is where Hund's rule gets into the picture. Hund's rule states that when electrons are distributed among orbitals of the same sublevel (like the 2p or 3d), each orbital gets one electron before any orbital gets a second. These single electrons must have parallel spins, meaning they spin in the same direction.

This rule aims to minimize electron repulsion since electrons have the same charge and repel each other. By spreading out before pairing up, the electrons remain as far from each other as possible, thus lowering the energy of the atom. When tackling problems related to orbital diagrams, always remember that if you have multiple empty orbitals at the same energy level, spread the electrons out before you start doubling them up in any orbital. For instance, with Chlorine's 3p sublevel, the first three electrons fill each of the three orbitals singly, respecting Hund's rule.

Pauli Exclusion Principle

The Pauli exclusion principle is all about individuality within the atomic world. It declares that no two electrons in an atom can have the same set of four quantum numbers. In simpler terms, an orbital can hold at most two electrons, and these two must have opposite spins. The quantum numbers determine the properties of the orbital an electron occupies, and by having opposite spins, the electrons are distinguished from one another.

Drawing from our earlier examples, look at orbital diagrams like the blueprint of a tiny, exclusive party where only opposite-'spinning' guests can pair up in any given space (orbital). The principle helps prevent overcrowding in any single orbital, which, in turn, governs the electron configurations of elements. While creating orbital diagrams, representing these opposite spins with arrows facing opposite directions helps you ensure compliance with the Pauli exclusion principle. For example, in a filled 1s orbital, you would see one arrow pointing up and the other pointing down within the same box.