Question

Write orbital diagrams for the valence electrons and indicate the number of unpaired electrons for each element. (a) Ne (b) \(\mathrm{I}\) (c) \(\mathrm{Sr}\) (d) \(\mathrm{Ge}\)

Short answer

Ne: no unpaired electrons; I: 1 unpaired electron; Sr: no unpaired electrons; Ge: 2 unpaired electrons.

Step-by-step solution

Understanding Orbital Diagrams

Orbital diagrams visualize the placement of electrons in an atom's orbitals. They depict the spin of electrons and help to identify unpaired electrons. Each orbital is represented by a box, with arrows indicating electron spins. To write an orbital diagram for the valence electrons, first determine the electron configuration of the atom and then place electrons in orbitals following Hund's rule (maximizing unpaired electrons) and the Pauli Exclusion Principle (each orbital can hold a maximum of two electrons with opposite spins).

Writing Orbital Diagrams for Element Ne

Neon (Ne) has an atomic number of 10, which gives it the electron configuration of 1s2 2s2 2p6. Its valence shell is the second shell (n=2), which is completely filled. The 2s orbital has two electrons with opposite spins while the 2p orbitals are completely filled with paired electrons. No unpaired electrons are present.

Writing Orbital Diagrams for Element I

Iodine (I) has an atomic number of 53. Its electron configuration ends with 5s2 4d10 5p5. Its valence shell is the fifth shell (n=5), which has seven electrons (2 in 5s, 5 in 5p). The 5s orbital is filled with paired electrons, while the three 5p orbitals have three electrons paired and one unpaired electron, adding up to one unpaired electron.

Writing Orbital Diagrams for Element Sr

Strontium (Sr) has an atomic number of 38 with the electron configuration ending in 5s2. Its valence shell electrons are the two in the 5s orbital. Both electrons in the 5s orbital are paired, resulting in no unpaired electrons.

Writing Orbital Diagrams for Element Ge

Germanium (Ge) has an atomic number of 32. Its electron configuration ends with 4s2 3d10 4p2. The valence shell is the fourth shell (n=4), which has four electrons (2 in 4s, 2 in 4p). The 4s orbital is filled with paired electrons. There are two unpaired electrons, one in each of the two 4p orbitals.

Key concepts

Valence Electrons

Valence electrons are the electrons in the outermost shell (energy level) of an atom. These electrons play a crucial role in chemical reactions and bonding because they can be gained, lost, or shared with other atoms. For example, in neon (Ne), the valence electrons are located in the second energy level, and there are eight of them, filling the level completely.

In constructing orbital diagrams, these are the electrons we focus on, as they determine the reactivity and bonding behavior of the element. For instance, iodine (I), which has seven valence electrons in its fifth shell, is much more reactive than neon and can form bonds by sharing its unpaired valence electron.

Unpaired Electrons

Unpaired electrons are those that are alone in an orbital without a corresponding electron with opposite spin. These electrons are significant because they make atoms more chemically reactive. In the case of iodine (I), there is one unpaired electron in the 5p orbital, as shown in the orbital diagram. This unpaired electron can participate in chemical bonding.

In contrast, neon (Ne) has no unpaired electrons since its valence shell is filled, making it chemically stable and unlikely to react. And as seen with strontium (Sr), the valence electrons are fully paired, resulting in no unpaired electrons, whereas germanium (Ge) has two, making it capable of forming chemical bonds.

Electron Configurations

The electron configuration of an element refers to the arrangement of electrons in an atom's orbitals. It is usually written using the aufbau principle, which states that electrons fill orbitals starting from the lowest energy level moving to higher ones. For example, neon's electron configuration is 1s2 2s2 2p6, indicating a filled valence shell.

Understanding the electron configuration is key to drawing orbital diagrams, as it tells you how many electrons are in each shell and subshell. The configurations for iodine, strontium, and germanium end with 5p5, 5s2, and 4p2, respectively, which are crucial in identifying the number of valence electrons and how these are distributed in different orbitals.

Hund's Rule

Hund's rule states that electrons will occupy separate orbitals in the same sublevel with parallel spins before pairing up. This minimizes electron repulsion and makes atoms more stable. When looking at an element like germanium (Ge), Hund's rule requires that its two unpaired 4p electrons occupy separate orbitals. They won't pair up until it is necessary to do so because all orbitals at that sublevel are half-filled.

This rule helps us draw accurate orbital diagrams by demonstrating the distribution of electrons within an orbital. Following Hund's rule results in the most stable arrangement of electrons within an atom.

Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two electrons within an atom can have the same set of four quantum numbers; in simpler terms, an atomic orbital may describe at most two electrons with opposing spins. In our step-by-step solutions, this principle ensures that the electrons in the neon 2s orbital, for instance, are paired with one pointing up and the other down.

When writing the orbital diagrams for valence electrons, each orbital is filled with one electron before any orbital gets a second electron, and when the second one is added, its spin must be opposite that of the first. This principle is fundamental in understanding the arrangement of electrons and their spins in orbital diagrams.