Question

Write the condensed electron configurations for the following atoms, using the appropriate noble-gas core abbreviations: \((\mathbf{a}) \mathrm{Cs},(\mathbf{b}) \mathrm{Ni},(\mathbf{c}) \mathrm{Se},(\mathbf{d}) \mathrm{Cd},(\mathbf{e}) \mathrm{U},(\mathbf{f}) \mathrm{Pb} .\)

Short answer

The condensed electron configurations for the given atoms are as follows: a) Cesium (Cs): \([Xe]\, 6s^1\) b) Nickel (Ni): \([Ar]\, 4s^2\, 3d^8 \) c) Selenium (Se): \([Ar]\, 4s^2\, 3d^{10}\, 4p^4 \) d) Cadmium (Cd): \([Kr]\, 5s^2\, 4d^{10} \) e) Uranium (U): \([Rn]\, 5f^3\, 6d^1\, 7s^2\) f) Lead (Pb): \([Xe]\, 4f^{14}\, 5d^{10}\, 6s^2\, 6p^2\)

Step-by-step solution

(Identify the noble gas core for each atom)

: We need to find the noble gases preceding each given atom in the periodic table. The noble gases are helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn). For each atom, locate the element in the periodic table, then identify the noble gas that comes before it.

(Write the electron configuration beyond the noble gas core)

: For each atom, write the electron configuration starting from the next principal energy level to the current principal energy level where the electrons reside. a) Cesium (Cs):

(Cs: Noble Gas Core)

: Cesium is located in Group 1 and Period 6 of the periodic table. Xenon (Xe) is the noble gas before it.

(Cs: Electron Configuration)

: Cs electron configuration beyond the noble gas core will start from principal energy level 6, which is the s-sublevel. Cesium has only one electron beyond the noble gas core. Thus, the complete electron configuration for cesium is \( [Xe]\, 6s^1\). b) Nickel (Ni):

(Ni: Noble Gas Core)

: Nickel is located in Group 10 and Period 4 of the periodic table. Argon (Ar) is the noble gas before it.

(Ni: Electron Configuration)

: Ni electron configuration beyond the noble gas core starts from the principal energy level 4. Nickel has 10 electrons beyond the noble gas core. Electron configuration for nickel is \( [Ar]\, 4s^2\, 3d^8 \). c) Selenium (Se):

(Se: Noble Gas Core)

: Selenium is located in Group 16 and Period 4 of the periodic table. Argon (Ar) is the noble gas before it.

(Se: Electron Configuration)

: Se electron configuration beyond the noble gas core starts from the principal energy level 4. Selenium has 16 electrons beyond the noble gas core. Electron configuration for selenium is \( [Ar]\, 4s^2\, 3d^{10}\, 4p^4 \). d) Cadmium (Cd):

(Cd: Noble Gas Core)

: Cadmium is located in Group 12 and Period 5 of the periodic table. Krypton (Kr) is the noble gas before it.

(Cd: Electron Configuration)

: Cd electron configuration beyond the noble gas core starts from the principal energy level 5. Cadmium has 12 electrons beyond the noble gas core. Electron configuration for cadmium is \( [Kr]\, 5s^2\, 4d^{10} \). e) Uranium (U):

(U: Noble Gas Core)

: Uranium is located in Group 3 and Period 7 of the periodic table but belongs to the f-block actinides series. Radon (Rn) is the noble gas before it.

(U: Electron Configuration)

: U electron configuration beyond the noble gas core starts from the principal energy level 7. Uranium has 3 electrons beyond the noble gas core, electron configuration for uranium is \( [Rn]\, 5f^3\, 6d^1\, 7s^2\). f) Lead (Pb):

(Pb: Noble Gas Core)

: Lead is located in Group 14 and Period 6 of the periodic table. Xenon (Xe) is the noble gas before it.

(Pb: Electron Configuration)

: Pb electron configuration beyond the noble gas core starts from the principal energy level 6. Lead has 14 electrons beyond the noble gas core. Electron configuration for lead is \( [Xe]\, 4f^{14}\, 5d^{10}\, 6s^2\, 6p^2\).

Key concepts

Noble Gas Core

When writing electron configurations for atoms, we often use the noble gas core to simplify the process. The noble gas core refers to the electron configuration of a noble gas that is filled before an element. Noble gases include helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn). They are known for having stable and complete electron shells.

By using the electron configuration of the nearest noble gas, which is fully filled, we can easily express the valence electron configuration. For instance, in cesium (Cs), the closest noble gas is xenon (Xe). Therefore, the electron configuration can start with \[Xe\]. This abbreviation signifies that all Xe electrons are present, and we only need to add the electrons beyond this point.

Principal Energy Level

Principal energy levels, or quantum levels, designate the main energy levels in an atom where electrons reside. Each level is denoted by a whole number, known as the quantum number \(n\). Electrons closest to the nucleus are in the lowest energy level, labeled \(n = 1\). As \(n\) increases, energy levels are further from the nucleus and have larger energy.

Each newly filled principal energy level can hold more electrons as \(n\) increases, such as the ones observed when writing configurations for cesium and lead. For example, cesium has its outermost electron in the 6th energy level or \(6s\).

Understanding which principal energy level electrons occupy helps in determining the electron configuration beyond the noble gas core, for instance, \(6s^1\) for Cs or \(4s^2 \ 3d^{10}\ 4p^4\) for Se.

Periodic Table

The periodic table is a systematic arrangement of elements, displaying them according to their atomic number and electron configurations. It is a powerful tool used to determine the electron configurations of elements. Elements are placed in order of increasing atomic number, arranged in rows or periods, correlating to principal energy levels.

Similarly, groups or columns contain elements with similar electron arrangements in their valence shells, influencing chemical properties. For example, elements in Group 1, like cesium (Cs), have one electron in their outer shell, making the simplified configuration start with \[Xe\], and then add \(6s^1\).

• By locating an element on the periodic table, you can identify both its electron configuration and its noble gas core.
• Finding cadmium (Cd) in Group 12 helps us verify its \[Kr \ 5s^2 \ 4d^{10}\].

The periodic table allows this quick access and constant verification of electron configurations.

Sublevel Notation

When describing an atom's electron configuration, we use sublevel notation to define where electrons are most likely to be found. Sublevels are marked by letters \(s, p, d,\) and \(f\), corresponding to electron cloud shapes and each can hold a set amount of electrons. For example,

• The \(s\) sublevel can hold 2 electrons.
• The \(p\) sublevel can hold up to 6 electrons.
• The \(d\) sublevel can hold up to 10 electrons.
• The \(f\) sublevel can hold up to 14 electrons.

Each sublevel is part of a principal energy level or quantum shell, with energy increasing as we move from \(s\) to \(f\).

In the case of nickel (Ni), the notation \[4s^2\ 3d^8\] includes both the \(s\) and \(d\) sublevel within the 4th principal energy level, capturing the idea that 2 electrons are in \(4s\) and 8 in \(3d\). Such notation gives a clear picture of how electrons are distributed within an atom's structure.