Question

Identify how many unpaired electrons are present in each of the following in the ground state: \(\mathrm{O}, \mathrm{O}^{+}, \mathrm{O}^{-}, \mathrm{Os}, \mathrm{Zr}, \mathrm{S}, \mathrm{F}, \mathrm{Ar}\).

Short answer

The number of unpaired electrons in each species in their ground state is as follows: \(\mathrm{O}\) (2), \(\mathrm{O}^+\) (3), \(\mathrm{O}^{-}\) (1), \(\mathrm{Os}\) (6), \(\mathrm{Zr}\) (2), \(\mathrm{S}\) (2), \(\mathrm{F}\) (1), and \(\mathrm{Ar}\) (0).

Step-by-step solution

Determine Electron Configurations

First, we need to determine the electron configurations for each species in their ground state. To do this, we look at their atomic numbers and fill the orbitals following the Aufbau principle, which states that we fill orbitals from lowest energy to highest energy (1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on). 1. \(\mathrm{O}\): Oxygen has an atomic number of 8, so its electron configuration is \(\mathrm{1s^2 2s^2 2p^4}\). 2. \(\mathrm{O}^+\): The positive charge indicates that one electron has been removed from the neutral oxygen atom. Thus, there are 7 electrons in the configuration, which is \(\mathrm{1s^2 2s^2 2p^3}\). 3. \(\mathrm{O}^{-}\): The negative charge indicates that one electron has been added to the neutral oxygen atom. Thus, there are 9 electrons in the configuration, which is \(\mathrm{1s^2 2s^2 2p^5}\). 4. \(\mathrm{Os}\): Osmium has an atomic number of 76, so its electron configuration is \(\mathrm{[Xe] 6s^2 4f^{14} 5d^6}\). Here, we use the noble gas shorthand to simplify the notation and show that the electron configuration is "complete" up to the previous noble gas in the periodic table, xenon, which has 54 electrons. 5. \(\mathrm{Zr}\): Zirconium has an atomic number of 40, so its electron configuration is \(\mathrm{[Kr] 5s^2 4d^2}\). 6. \(\mathrm{S}\): Sulfur has an atomic number of 16, so its electron configuration is \(\mathrm{1s^2 2s^2 2p^6 3s^2 3p^4}\). 7. \(\mathrm{F}\): Fluorine has an atomic number of 9, so its electron configuration is \(\mathrm{1s^2 2s^2 2p^5}\). 8. \(\mathrm{Ar}\): Argon has an atomic number of 18, so its electron configuration is \(\mathrm{1s^2 2s^2 2p^6 3s^2 3p^6}\).

Identify the Unpaired Electrons

Next, we need to count the number of unpaired electrons in each species' ground state electron configuration, focusing on the highest energy orbitals. 1. \(\mathrm{O}\): In \(\mathrm{2p^4}\), there are two unpaired electrons since we can have a maximum of two electrons with the same spin in each orbital. 2. \(\mathrm{O}^+\): In \(\mathrm{2p^3}\), there are three unpaired electrons, as the three electrons with the same spin occupy all three orbitals. 3. \(\mathrm{O}^{-}\): In \(\mathrm{2p^5}\), there is only one unpaired electron. 4. \(\mathrm{Os}\): There are six unpaired electrons in \(\mathrm{5d^6}\) orbitals. 5. \(\mathrm{Zr}\): In the electron configuration \(\mathrm{4d^2}\), there are two unpaired electrons. 6. _\(\mathrm{S}\):_ In \(\mathrm{3p^4}\), there are two unpaired electrons. 7. \(\mathrm{F}\): In \(\mathrm{2p^5}\), there is only one unpaired electron. 8. \(\mathrm{Ar}\): In this configuration, all the electrons are paired, so there are 0 unpaired electrons. In conclusion, the number of unpaired electrons in each species in their ground state is as follows: \(\mathrm{O}\) (2), \(\mathrm{O}^+\) (3), \(\mathrm{O}^{-}\) (1), \(\mathrm{Os}\) (6), \(\mathrm{Zr}\) (2), \(\mathrm{S}\) (2), \(\mathrm{F}\) (1), and \(\mathrm{Ar}\) (0).

Key concepts

Unpaired Electrons

Unpaired electrons are electrons that reside in atomic or molecular orbitals alone, without a partner with opposite spin. Understanding unpaired electrons is crucial for predicting the magnetic properties and reactivity of an element or compound.

• Magnetic properties: Atoms with unpaired electrons are typically paramagnetic. This means they are attracted to magnetic fields. The more unpaired electrons, the stronger the attraction.
• Chemical reactivity: Unpaired electrons can participate in chemical reactions. They often seek to pair up, which can make certain atoms more reactive.

When determining the number of unpaired electrons in an element, particularly for the elements mentioned in the original exercise, focus on the highest energy level where electrons are less likely to pair. For example, in the oxygen atom, the 2p orbital has two unpaired electrons because only two of the three p orbitals are fully filled with opposite-spin pairs.

Aufbau Principle

The Aufbau principle is a fundamental rule for determining the electron configuration of atoms in their ground state. According to this principle, electrons fill atomic orbitals starting with the lowest energy levels before moving to higher ones.

• Sequence of filling: Electrons begin filling the 1s orbital, the lowest in energy, then proceed to 2s, then 2p, and so forth, following the order of increasing energy.
• Building up: The name "Aufbau" literally means "building up" in German, as electrons build up in the lowest available energy states to achieve the most stable configuration.
• Pauli Exclusion Principle: Each orbital can hold a maximum of two electrons with opposite spins, due to the Pauli exclusion principle.

In practice, this principle helps us create an electron configuration for an element. For example, by using the order established by the Aufbau principle, you can determine the electron configuration of oxygen as 1s² 2s² 2p⁴, filling from lowest to highest energy levels.

Ground State

The ground state of an atom is its lowest energy state, where electrons are arranged in the most stable configuration. Every atom seeks to be in its ground state naturally.

• Stable and unexcited: In the ground state, an atom is at its lowest potential energy. Electrons occupy the lowest energy orbitals available.
• Predicting behavior: Knowing the ground state of an atom allows scientists to predict how it will react with other atoms or molecules.
• Common reference: The ground state serves as a reference point for studying excited states, where atoms absorb energy, causing one or more electrons to move to higher energy levels.

Using the ground state configuration, such as [Xe] 6s² 4f¹⁴ 5d⁶ for Osmium, chemists can understand its chemical characteristics and reactivity based on its filled and unfilled orbitals.