Question

Write electron configurations for each element. Use the symbol of the previous noble gas in brackets to represent the core electrons. (a) Ga (b) As (c) \(\mathrm{Rb}\) (d) \(S n\)

Short answer

(a) Ga: [Ar]3d^{10}4s^{2}4p^{1}(b) As: [Ar]3d^{10}4s^{2}4p^{3}(c) Rb: [Kr]5s^{1}(d) Sn: [Kr]4d^{10}5s^{2}5p^{2}

Step-by-step solution

Identify the Previous Noble Gas

For each element, find the noble gas that precedes it on the periodic table. This noble gas will represent the core electrons for the element's electron configuration.

Write the Electron Configuration for Gallium (Ga)

The previous noble gas before Ga (atomic number 31) is Ar (Argon, atomic number 18). Starting from Argon, write out the remaining electrons in the order of the orbital filling sequence: 3d^10 4s^2 4p^1.

Write the Electron Configuration for Arsenic (As)

For As (atomic number 33), use the previous noble gas Ar. The configuration from Arsenic, after Argon, is: 3d^10 4s^2 4p^3.

Write the Electron Configuration for Rubidium (Rb)

The previous noble gas before Rb (atomic number 37) is Kr (Krypton, atomic number 36). Since Rubidium is one element past Krypton, its electron configuration includes all of Krypton's electrons plus one additional electron: 5s^1.

Write the Electron Configuration for Tin (Sn)

Tin (Sn, atomic number 50) comes after the noble gas Kr. The electron configuration from Tin, starting after Krypton, is: 4d^10 5s^2 5p^2.

Key concepts

Orbital Filling Sequence

Understanding the orbital filling sequence is crucial to writing electron configurations. This sequence indicates the order in which orbitals are filled with electrons. Electrons are distributed according to the increasing energy levels of the orbitals, which is summarized by the Aufbau principle. A helpful tool in learning this sequence is the diagonal rule or the use of a mnemonic, where the order of filling starts from 1s, then 2s, 2p, 3s, 3p, and so forth.

This order is determined by factors such as the shape of the orbital, which translates to different energy levels in the subshells. For example, even though the 4s subshell belongs to the fourth energy level, it is filled before the 3d subshell because it has a lower energy. The standard notation reflects this sequence: for gallium (Ga), after the [Ar] core, the electrons fill the 3d orbitals before the 4s and 4p. Remember, the order follows: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p, and so on, as you move across periods and down groups on the periodic table.

Noble Gas Notation

The noble gas notation is a shorthand approach to writing electron configurations. Since noble gases have complete electron shells, they serve as a reference point for other elements. This method simplifies writing long electron configurations, emphasizing the valence electrons which are crucial for chemical properties.For instance, when we write the electron configuration of arsenic (As), starting with [Ar], we are noting that As has the same core electron configuration as argon, which is the last noble gas before arsenic in the periodic table. The electrons that come after [Ar] are unique to arsenic and describe its position in the periodic table as well as its chemical behavior. The noble gas notation effectively simplifies the electron configuration, showing the mostly unreactive core electrons as a noble gas and the reactive valence electrons in an expanded form.

Periodic Table

The periodic table is not just a chart of elements, but a profound tool for understanding electron configurations. Elements are arranged in periods (rows) and groups (columns) based on their atomic number, which is directly related to the number of protons and electrons an atom has. Moving from left to right across a period, each element has one more electron and one more proton than the one before. This incremental change affects the way electrons are organized around the nucleus.

When determining the electron configurations, the periodic table guides us to identify the number of electrons in an element, the previous noble gas (used for the noble gas notation), and the order of the orbital filling sequence. For example, rubidium (Rb) is located after krypton (Kr) on the periodic table, and therefore rubidium's electron configuration starting point after [Kr] will be the 5s subshell, consistent with its position on the table.

Atomic Number

The atomic number is the number of protons an atom has and defines each element in the periodic table. It also indicates the total number of electrons an atom has when it is in a neutral state. With each step up in atomic number, a corresponding electron is added to an atom's electron configuration. For example, as we step from gallium (Ga) with an atomic number of 31 to germanium (Ge) with an atomic number of 32, one electron is added, changing the electron configuration.

In the context of electron configurations, the atomic number not only tells us how many electrons we need to account for but also guides us through the orbital filling sequence. Tin (Sn), for example, with an atomic number of 50, will have 50 electrons arranged according to the same sequence of orbital filling. With the atomic number, students can visually and numerically connect the element to its specific place on the periodic table and its detailed electron configuration.