Question

Write the abbreviated electron configuration of the \(\mathrm{Mn}^{3+}\) ion. How many unpaired electrons does the ion contain?

Short answer

The abbreviated electron configuration of \(\mathrm{Mn}^{3+}\) is \([Ar] 3d^4\), and the ion contains four unpaired electrons.

Step-by-step solution

Identify the Atomic Number of Manganese (Mn)

Find the atomic number of Manganese (Mn) to determine the number of electrons in a neutral manganese atom. The atomic number of Manganese is 25, which means a neutral Mn atom has 25 electrons.

Account for the Charge on the Ion

Determine the number of electrons in the \(\mathrm{Mn}^{3+}\) ion. Since it is a 3+ ion, it has lost three electrons. Subtract three from the atomic number of Mn to find the remaining number of electrons: 25 - 3 = 22 electrons.

Write the Electron Configuration of the Neutral Mn

Write the full electron configuration for a neutral manganese atom. For Mn with 25 electrons, the electron configuration is: \([Ar] 3d^5 4s^2\).

Modify the Configuration for \(\mathrm{Mn}^{3+}\)

Remove three electrons to reflect the charge of the ion. The electrons are removed according to the Aufbau principle, from the outermost orbitals first. In this case, two electrons are removed from the 4s orbital and one electron from the 3d orbital: \([Ar] 3d^5 4s^2\) becomes \([Ar] 3d^4\) for \(\mathrm{Mn}^{3+}\).

Determine the Number of Unpaired Electrons

Count the number of unpaired electrons in the 3d subshell for \(\mathrm{Mn}^{3+}\). Since we have \([Ar] 3d^4\), there are four electrons in the 3d subshell. According to Hund's Rule, these electrons will occupy separate orbitals as far as possible before pairing up. Thus, there are four unpaired electrons.

Key concepts

Atomic Number

The atomic number is a fundamental concept in chemistry and physics. It represents the number of protons found in the nucleus of an atom. This number uniquely identifies a chemical element and determines its position in the periodic table. For instance, Manganese (Mn) has an atomic number of 25, meaning it has 25 protons in its nucleus. The atomic number also tells us the number of electrons in a neutral atom, as the number of electrons equals the number of protons to balance the electrical charge.

When dealing with ions, like \(\mathrm{Mn}^{3+}\), knowing the atomic number helps us to first determine the electron configuration of the neutral atom. From there, we can understand how the ion's electron configuration will differ from the neutral state due to the gain or loss of electrons, resulting in a positive or negative charge respectively.

Aufbau Principle

The Aufbau Principle is a guideline to the electronic structure of atoms. According to this principle, electrons occupy orbitals starting from the lowest energy level and move towards higher energy levels. This 'building-up' process helps us predict how electrons fill up the atomic orbitals. It offers a way to write the electron configurations systematically, starting from the 1s orbital and proceeding through 2s, 2p, 3s, and so on, following the energy levels.

In the context of ions like \(\mathrm{Mn}^{3+}\), when electrons are removed to form a positively charged ion, they are typically removed from the orbitals with the highest energy first, which can be understood through the electron configuration based on the Aufbau Principle. This rule explains why in the solution, electrons are removed from the 4s orbital before the 3d orbital when forming \(\mathrm{Mn}^{3+}\).

Hund's Rule

Hund's Rule addresses the distribution of electrons across orbitals of the same energy. According to this rule, electrons will fill each degenerate orbital singly before any orbital gets a second electron, and all singly occupied orbitals will have electrons with the same spin to maximize total spin. This concept is critical when picturing an atom's electronic arrangement, especially in multi-electron systems.

When considering unpaired electrons in the \(\mathrm{Mn}^{3+}\) ion's \(3d\) subshell, Hund's Rule explains why there are four unpaired electrons. The rule advises that these four electrons occupy separate \(3d\) orbitals first, keeping their spins parallel, before any pairing occurs. This principle is key to predicting magnetic properties and understanding electron arrangements in ions and atoms.

Unpaired Electrons

Unpaired electrons are those that are alone in an atomic or molecular orbital and are not coupled with another electron with an opposite spin. The presence of unpaired electrons can affect the magnetic properties of an ion or atom. An atom or ion with unpaired electrons is typically paramagnetic, meaning it is attracted by a magnetic field, while species with all paired electrons are diamagnetic, and repel a magnetic field.

In the \(\mathrm{Mn}^{3+}\) ion, we find four unpaired electrons by applying the Aufbau Principle and Hund's Rule to the \(3d\) orbital. The ion's paramagnetic nature arises due to these unpaired electrons, which have important implications in material science and chemistry.

Orbital Notation

Orbital notation is a visual method for expressing the electron configuration of an atom or ion. It uses lines (or boxes) to represent orbitals and arrows to depict electrons. The direction of the arrow indicates the electron's spin (up or down). This notation goes hand-in-hand with the Aufbau Principle and Hund's Rule, illustrating how electrons are distributed among the available orbitals.

For the \(\mathrm{Mn}^{3+}\) ion, the orbital notation will show the \(3d\) subshell having four single arrows (representing electrons) pointing in the same direction, indicating four unpaired electrons, each in a separate \(3d\) orbital. By understanding how to interpret orbital notation, students can more easily grasp the distribution and pairing of electrons within an atom or ion.