Question

Write orbital diagrams for each ion and determine if the ion is diamagnetic or paramagnetic. $$ \text { a. } \mathrm{Cd}^{2+} \quad \text { b. } \mathrm{Au}^{+} \quad \text { c. } \mathrm{Mo}^{3+} \quad \text { d. } \mathrm{Zr}^{2+} $$

Short answer

Cd\(^{2+}\) is diamagnetic with the electron configuration [Kr]4d\(^{10}\). Au\(^{+}\) is diamagnetic with the electron configuration [Xe]4f\(^{14}\)5d\(^{9}\). Mo\(^{3+}\) is paramagnetic with the electron configuration [Kr]4d\(^{3}\). Zr\(^{2+}\) is diamagnetic with the electron configuration [Kr]4d\(^{2}\).

Step-by-step solution

- Write Electron Configuration of Neutral Atoms

Before considering the ions, write the electron configurations of the neutral atoms. Use the periodic table to determine the number of electrons for each element: Cd (Cadmium) with atomic number 48, Au (Gold) with atomic number 79, Mo (Molybdenum) with atomic number 42, and Zr (Zirconium) with atomic number 40.

- Write Electron Configuration of Ions

Adjust the electron configuration for each atom to reflect the loss of electrons due to the ion charge. Cd loses 2 electrons, Au loses 1 electron, Mo loses 3 electrons, and Zr loses 2 electrons.

- Draw Orbital Diagrams for Each Ion

Using the electron configurations from Step 2, draw the orbital diagrams for each ion. Place the electrons in the orbitals following Hund’s rule and the Pauli exclusion principle.

- Determine Diamagnetic or Paramagnetic

Examine each ion's orbital diagram. An ion is diamagnetic if all electrons are paired. If there are unpaired electrons, the ion is paramagnetic.

Key concepts

Electron Configuration

Understanding electron configuration is essential for mapping out the distribution of electrons around an atom's nucleus. Electrons are arranged in energy levels, sublevels, and orbitals according to increasing energy. Each orbital can hold a maximum of two electrons.

The configuration is noted using numbers (representing energy levels), letters (representing sublevels), and superscripts (indicating the number of electrons in those sublevels). For example, hydrogen has an electron configuration of 1s¹, and helium is 1s². When dealing with ions, the process simply adjusts for the gain or loss of electrons. In our exercises, cations such as Cd²⁺ or Au⁺ would have their outermost electrons removed in the configuration that corresponds to their charge.

Diamagnetic and Paramagnetic Ions

The magnetic properties of an ion can be categorized into two types: diamagnetic and paramagnetic, which depend on the presence of unpaired electrons in the ion's electron configuration.

• Diamagnetic ions have all their electrons paired and are repelled by a magnetic field. These ions have an even number of electrons or have filled sublevels in their electron configuration.
• Paramagnetic ions possess at least one unpaired electron, causing them to be attracted by a magnetic field. This occurs when an ion has an odd number of electrons or partially filled sublevels.

For example, by determining the electron configurations in our exercise, we can identify that an ion like Cd²⁺ is diamagnetic if all its electrons are paired after losing two electrons.

Hund's Rule

Hund's rule addresses how electrons are distributed among orbitals of the same sublevel. The rule states that every orbital in a sublevel is singly occupied before it is doubly occupied. Electrons also maintain parallel spins due to their repulsive forces when occupying these orbitals.

When applying Hund's rule to our exercise, for instance, in Mo³⁺, we would first single-occupy every 4d orbital before any are doubly occupied. This approach minimizes electron repulsion and is essential for correctly drawing the orbital diagrams.

Pauli Exclusion Principle

The Pauli exclusion principle is a fundamental rule in quantum mechanics which states that no two electrons in an atom can have an identical set of all four quantum numbers. Essentially, this means that each electron must have a unique position in an atom's orbitals.

For an orbital diagram, this translates to a maximum of two electrons occupying each orbital, and they must have opposite spins. In a box-and-arrow orbital diagram, this is depicted as arrows pointing in opposite directions. In our ion electron configurations, for example, Zr²⁺, this principle ensures the correct pairing and placement of electrons in orbitals.