Question

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

Short answer

The number of unpaired electrons in each atom/ion in their ground state is as follows: O: 2; O⁺: 1; O⁻: 1; Os: 2; Zr: 0; S: 2; F: 1; and Ar: 0.

Step-by-step solution

Atomic Numbers

To determine the atomic number (Z), consult a periodic table. The atomic number corresponds to the number of protons and electrons in a neutral atom. \(\mathrm{O}\): Atomic number (Z) = 8 \(\mathrm{O}^+\): Z = 8, but since it has a +1 charge, it has one less electron, so 7 electrons. \(\mathrm{O}^-\): Z = 8, but since it has a -1 charge, it has one additional electron, so 9 electrons. \(\mathrm{Os}\): Z = 76 \(\mathrm{Zr}\): Z = 40 \(\mathrm{S}\): Z = 16 \(\mathrm{F}\): Z = 9 \(\mathrm{Ar}\): Z = 18 **Step 2: Write electron configurations**

Electron Configurations

Using the Aufbau principle, Hund's rule, and Pauli exclusion principle, we can write the electron configurations for each atom/ion. \(\mathrm{O}\): 1s²2s²2p⁴ \(\mathrm{O}^+\): 1s²2s²2p³ \(\mathrm{O}^-\): 1s²2s²2p⁵ \(\mathrm{Os}\): 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶6s²4f¹⁴5d⁶ \(\mathrm{Zr}\): 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d² \(\mathrm{S}\): 1s²2s²2p⁶3s²3p⁴ \(\mathrm{F}\): 1s²2s²2p⁵ \(\mathrm{Ar}\): 1s²2s²2p⁶3s²3p⁶ **Step 3: Count the unpaired electrons**

Unpaired Electrons

Look for unpaired electrons in each electron configuration. \(\mathrm{O}\): 2p⁴ contains two unpaired electrons (↑↓, ↑, ↑). \(\mathrm{O}^+\): 2p³ contains one unpaired electron (↑↓, ↑, ↑). \(\mathrm{O}^-\): 2p⁵ contains one unpaired electron (↑↓, ↑↓, ↑). \(\mathrm{Os}\): 5d⁶ contains two unpaired electrons (↑↔, ↑↔, ↑↔, ↑, ↑, -). \(\mathrm{Zr}\): 4d² contains no unpaired electrons (↑↓, -). \(\mathrm{S}\): 3p⁴ contains two unpaired electrons (↑↓, ↑, ↑). \(\mathrm{F}\): 2p⁵ contains one unpaired electron (↑↓, ↑↓, ↑). \(\mathrm{Ar}\): No unpaired electrons. Therefore, the number of unpaired electrons in each atom/ion is: O: 2; O⁺: 1; O⁻: 1; Os: 2; Zr: 0; S: 2; F: 1; and Ar: 0

Key concepts

Electron Configuration

The electron configuration of an atom describes the distribution of electrons among the various orbitals of an atom. It helps us understand the electronic structure and is crucial for predicting chemical behavior and bonding.
Electrons are organized into shells and subshells, with each having a capacity limit. We follow the Aufbau principle, which tells us to fill the lowest energy orbitals first.

• The Pauli Exclusion Principle states each orbital can hold a maximum of two electrons with opposite spins.
• Hund's Rule tells us that we fill degenerate (same energy) orbitals singly first before pairing electrons.

For example, oxygen in its ground state has the electron configuration: 1s²2s²2p⁴. This means that the first shell is fully occupied, and the second shell has 6 electrons distributed across its s and p orbitals.

Atomic Number

The atomic number, often denoted Z, is the number of protons contained in the nucleus of an atom. It uniquely identifies a chemical element and defines its position in the periodic table.
The atomic number is crucial because it also indicates the total number of electrons in a neutral atom, which directly influences its chemical properties.

• Different isotopes of an element share the same atomic number but vary in neutron count.
• For ions, the atomic number remains the same, though the electron count changes depending on the charge.

For instance, oxygen has an atomic number of 8, meaning a neutral oxygen atom possesses 8 electrons.

Ground State Electron Configuration

The ground state electron configuration of an atom or an ion refers to its lowest energy state. In this configuration, electrons are filled into orbitals following specific rules to achieve a state of minimum energy.

• Anything different from the ground state configuration indicates a more energetic excited state.
• The ground state stabilizes atoms and determines the number of unpaired electrons, critical for chemical reactions and magnetism.

Using the ground state electron configuration, we determine the unpaired electrons, such as oxygen with 2 unpaired electrons in its 2p orbital.

Periodic Table

The periodic table is a systematic arrangement of all known chemical elements. Elements are organized by increasing atomic number, which aligns them according to similar chemical properties.
Columns, known as groups, contain elements sharing chemical and physical traits, while rows, or periods, indicate elements that fill the same principal quantum shell.

• The table is divided into blocks (s-block, p-block, d-block, f-block) based on the subshell in which the last electron resides.
• It is an essential tool for predicting the behavior and properties of elements based on their position.

For example, elements like oxygen and fluorine, both in the p-block, exhibit non-metallic character and high electronegativity.

Orbitals

An orbital is a region around an atom's nucleus where electrons are likely to be found. It is described by quantum numbers derived from solutions of the Schrödinger equation.
Orbitals come in various shapes – s, p, d, and f – each capable of holding different numbers of electrons:

• s orbital is spherical and holds up to 2 electrons.
• p orbitals are dumbbell-shaped and can hold up to 6 electrons across three p orbitals.
• d orbitals, though more complex in shape, can hold up to 10 electrons spread over five orbitals.

The concept of orbitals is crucial for understanding the electron configuration, as it determines how electrons are spatially distributed and contributes to chemical bonding and molecular geometry.