Question

Draw orbital diagrams for the abbreviated configurations of (a) \(\mathrm{Ni},(\mathbf{b}) \mathrm{Cs},(\mathbf{c}) \mathrm{Ge},\) and \((\mathbf{d}) \mathrm{Br}\)

Short answer

Nickel (Ni): [Ar] 3d^8 4s^2 with 3d orbitals partially filled and 4s full. Cesium (Cs): [Xe] 6s^1 with 6s orbital singly filled. Germanium (Ge): [Ar] 3d^10 4s^2 4p^2 with 3d orbitals full, 4s full, and 4p partially filled. Bromine (Br): [Ar] 3d^10 4s^2 4p^5 with 3d orbitals full, 4s full, and 4p nearly full.

Step-by-step solution

Understand Noble Gas Abbreviation

The noble gas abbreviation simplifies the electron configurations of elements by starting with the electron configuration of the closest noble gas with a lower atomic number, then adding the additional electrons for the element in question.

Write out Abbreviated Electron Configurations for Each Element

Find the noble gas preceding each element in the periodic table and then write the remaining electron configuration. For Nickel (Ni), the preceding noble gas is Argon (Ar), so the configuration starts with [Ar]. For Cesium (Cs), it's Xenon (Xe). For Germanium (Ge), it's Argon (Ar). For Bromine (Br), it's Argon (Ar).

Draw the Orbital Diagrams for Each Element

Using the abbreviated electron configurations, draw the additional electron orbitals as boxes with arrows representing the electrons. Follow Hund's Rule (maximize unpaired electrons in orbitals of the same energy before pairing) and the Pauli Exclusion Principle (each orbital can hold a maximum of two electrons with opposing spins).

Draw Orbital Diagram for Nickel (Ni)

Nickel (Ni), atomic number 28: Abbreviated configuration of [Ar] 3d^8 4s^2. The 3d sublevel has eight electrons, and the 4s sublevel has two electrons. Draw five 3d orbitals and fill them with electrons, pairing when necessary, then draw the 4s orbital and fill it with two electrons.

Draw Orbital Diagram for Cesium (Cs)

Cesium (Cs), atomic number 55: Abbreviated configuration of [Xe] 6s^1. The 6s sublevel has one electron. Draw the 6s orbital and place one electron in it.

Draw Orbital Diagram for Germanium (Ge)

Germanium (Ge), atomic number 32: Abbreviated configuration of [Ar] 3d^10 4s^2 4p^2. The 3d sublevel is fully filled with ten electrons, the 4s sublevel has two electrons, and the 4p sublevel has two electrons. Draw and fill the orbitals accordingly.

Draw Orbital Diagram for Bromine (Br)

Bromine (Br), atomic number 35: Abbreviated configuration of [Ar] 3d^10 4s^2 4p^5. The 3d sublevel is fully filled with ten electrons, the 4s sublevel has two, and the 4p sublevel has five electrons. Draw and fill the orbitals accordingly, with one orbital in the 4p sublevel containing a single electron.

Key concepts

Electron Configuration

Understanding electron configuration is essential for chemistry students, as it provides insight into the distribution of electrons in an atom's energy levels. A proper electron configuration will list the energy levels and sublevels in the order of filling, corresponding to how electrons populate an atom's orbitals.

For example, the electron configuration for Nickel (Ni) starts with the noble gas preceding it, Argon (Ar). We then add the additional electrons to the configuration, resulting in [Ar] 3d⁸ 4s². Every element in the periodic table follows this pattern, filling each sublevel according to the energy and number of available orbitals, such as s, p, d, and f.

It's crucial to understand the sequence in which these orbitals fill up, as it affects chemical properties and bonding. The 'Aufbau Principle' helps predict the order, which is often demonstrated in diagrams or tables to guide students.

Hund's Rule

Hund's Rule is an important principle when drawing orbital diagrams. It's like ensuring each seat in a cinema row is partially filled before anyone has to share.

When electrons are placed into a set of orbitals of equal energy, they are spread out as much as possible to give unpaired electrons before any pairing occurs. This maximizes the total spin, resulting in the lowest energy configuration for the electrons in a subshell. For instance, when filling the p orbitals, you would place one electron in each of the three orbitals before starting to pair them up. This rule explains the unpaired electrons in elements, which further dictate their magnetic properties and how they interact with other atoms.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a quantum mechanical phenomenon that forms the basis for many electron arrangement predictions. It states that no two electrons in an atom can have the same set of four quantum numbers. Simply put, an orbital can hold a maximum of two electrons, and those two must have opposite spins.

This principle is represented in orbital diagrams by the arrows pointing in opposite directions. When drawing the diagrams for the exercise elements such as Nickel (Ni) and Bromine (Br), we observe that after applying Hund's Rule, we pair electrons in the same orbital with opposite spins, ensuring compliance with the Pauli Exclusion Principle.

Noble Gas Abbreviation

The noble gas abbreviation is a shorthand notation in electron configurations that simplifies how we communicate the arrangement of an atom's electrons. By starting with a noble gas (like Argon [Ar] or Xenon [Xe]), which has a completed outer shell, we then add the extra electrons needed to reach the element in question.

For instance, Cesium (Cs), which follows Xenon (Xe) in the periodic table, has the noble gas abbreviation of [Xe] followed by the remaining configuration 6s¹. This makes it much easier to write and understand, especially for elements with many electrons. This method emphasizes the importance of noble gases as they are the 'milestones' in the periodic table, reflecting the full and stable electron configurations that other elements 'build upon'.