Question

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

Short answer

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

Step-by-step solution

Write electron configurations

Write the electron configuration for each species in the ground state as follows: \(\mathrm{O}: 1s^2 \ 2s^2 \ 2p^4\) \(\mathrm{O}^{+}: 1s^2 \ 2s^2 \ 2p^3\) \(\mathrm{O}^{-}: 1s^2 \ 2s^2 \ 2p^5\) \(\mathrm{Os}(Z=76): 1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 4s^2 \ 3d^{10} \ 4p^6 \ 5s^2 \ 4d^{10} \ 5p^6 \ 6s^2 \ 4f^{14} \ 5d^6\) \(\mathrm{Zr}(Z=40): 1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 4s^2 \ 3d^{10} \ 4p^6 \ 5s^2 \ 4d^2\) \(\mathrm{S}: 1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^4\) \(\mathrm{F}: 1s^2 \ 2s^2 \ 2p^5\) \(\mathrm{Ar}: 1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6\)

Identify partially-filled orbitals

Identify the partially-filled orbitals in each electron configuration: \(\mathrm{O}: 2p^4\) \(\mathrm{O}^{+}: 2p^3\) \(\mathrm{O}^{-}: 2p^5\) \(\mathrm{Os}: 5d^6\) \(\mathrm{Zr}: 4d^2\) \(\mathrm{S}: 3p^4\) \(\mathrm{F}: 2p^5\) \(\mathrm{Ar}: \text{All orbitals are filled.}\)

Count unpaired electrons

Count the number of unpaired electrons in the partially-filled orbitals: \(\mathrm{O}: 2\) unpaired electrons \(\mathrm{O}^{+}: 1\) unpaired electron \(\mathrm{O}^{-}: 3\) unpaired electrons \(\mathrm{Os}: 2\) unpaired electrons \(\mathrm{Zr}: 2\) unpaired electrons \(\mathrm{S}: 2\) unpaired electrons \(\mathrm{F}: 1\) unpaired electron \(\mathrm{Ar}: 0\) unpaired electrons Thus, the number of unpaired electrons in each species in the ground state is: \(\mathrm{O}: 2\) \(\mathrm{O}^{+}: 1\) \(\mathrm{O}^{-}: 3\) \(\mathrm{Os}: 2\) \(\mathrm{Zr}: 2\) \(\mathrm{S}: 2\) \(\mathrm{F}: 1\) \(\mathrm{Ar}: 0\)

Key concepts

Electron Configurations

Understanding electron configurations is essential for describing the positions of electrons in an atom's energy levels. The configuration follows the Pauli exclusion principle and Hund's rule, ensuring that no two electrons can have the same set of four quantum numbers, and that every orbital in a subshell is singly occupied before any orbital is doubly occupied.

Electron configurations are noted by listing the energy levels and orbitals, along with the number of electrons present in each—for example, \(1s^2 2s^2 2p^4\) for oxygen. These configurations help in predicting chemical properties, such as bonds an atom can form and its magnetism. The arrangement of electrons in increasingly higher energy levels (orbitals) explains much about an atom's reactive behavior.

When a configuration is written for an ion, it's adjusted to reflect the gain or loss of electrons. This is evident in the exercise, where oxygen (\(O\)), the oxide ion (\(O^-\)), and the oxonium ion (\(O^+\)) have different configurations due to their difference in electron count.

Partially-Filled Orbitals

Partially-filled orbitals arise when there are not enough electrons to completely fill all the orbitals in a subshell. According to Hund's rule, electrons will first fill these orbitals singly and with parallel spins. A partially-filled orbital can thus give information about an element's magnetic properties and chemical reactivity.

For instance, in oxygen's electron configuration (\(2p^4\)), the six available p-orbitals are not completely filled, leading to two unpaired electrons. These unpaired electrons are significant in chemical bonding and magnetism. Elements with partially-filled orbitals are often paramagnetic, meaning they are attracted into a magnetic field due to these unpaired electrons.

Ground State

The ground state of an atom is its lowest energy state, where all electrons occupy the lowest possible energy levels according to the aufbau principle. An atom will naturally fall to this state and can transition to an excited state when energy is absorbed, pushing an electron to a higher energy level.

In the context of the exercise, identifying the ground state electron configurations of various elements enables the counting of unpaired electrons. As atoms strive to be in the ground state, understanding this configuration forms the basis for predicting the chemical nature and the type of bonds an atom or ion might form.

Quantum Numbers

Quantum numbers are like addresses that give the location of electrons within an atom. Each electron in an atom is defined by a unique set of four quantum numbers: the principal (\(n\)), azimuthal (\(l\)), magnetic (\(m_l\)), and spin (\(m_s\)) quantum numbers.

The principal quantum number (\(n\)) denotes the energy level of an electron, the azimuthal quantum number (\(l\)) defines the subshell (s, p, d, f), and the magnetic quantum number (\(m_l\)) specifies an individual orbital within that subshell. The spin quantum number (\(m_s\)) indicates the direction of the electron's spin and can only have values of +1/2 or -1/2, reflecting the spin's orientation. These numbers not only define the electron's location but also explain the atomic orbitals' shape, orientation, and the electrons' spin.