Question

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

Short answer

(a) Cs: \[[\mathrm{Xe}] 6s^1\] (b) Ni: \[[\mathrm{Ar}] 4s^2 3d^8\] (c) Se: \[[\mathrm{Ar}] 4s^2 3d^{10} 4p^4\] (d) Cd: \[[\mathrm{Kr}] 5s^2 4d^{10}\] (e) U: \[[\mathrm{Rn}] 5f^3 6d^1 7s^2\] (f) Pb: \[[\mathrm{Xe}] 6s^2 4f^{14} 5d^{10} 6p^2\]

Step-by-step solution

(a) Cs - Cesium

First, find the electron configuration of Cesium by using a periodic table. Cesium has an atomic number of 55, which means it has 55 electrons. Its electron configuration can be written as: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^1\] Now, find the appropriate noble-gas abbreviation. Xenon (Xe) has an atomic number of 54 and sits right before Cs in the periodic table, with its electron configuration: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6\] Using the noble-gas core abbreviation for xenon, the condensed electron configuration for Cesium is: \[[\mathrm{Xe}] 6s^1\]

(b) Ni - Nickel

First, find the electron configuration of Nickel using a periodic table. Nickel has an atomic number of 28, which means it has 28 electrons. Its electron configuration can be written as: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^8\] Now, find the appropriate noble-gas abbreviation. Argon (Ar) has an atomic number of 18 and sits right before the transition metals, where Nickel is found. Argon's electron configuration is: \[1s^2 2s^2 2p^6 3s^2 3p^6\] Using the noble-gas core abbreviation for argon, the condensed electron configuration for Nickel is: \[[\mathrm{Ar}] 4s^2 3d^8\]

(c) Se - Selenium

First, find the electron configuration of Selenium using a periodic table. Selenium has an atomic number of 34, which means it has 34 electrons. Its electron configuration can be written as: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^4\] Now, find the appropriate noble-gas abbreviation. Argon (Ar) has an atomic number of 18, and its electron configuration is: \[1s^2 2s^2 2p^6 3s^2 3p^6\] Using the noble-gas core abbreviation for argon, the condensed electron configuration for Selenium is: \[[\mathrm{Ar}] 4s^2 3d^{10} 4p^4\]

(d) Cd - Cadmium

First, find the electron configuration of Cadmium using a periodic table. Cadmium has an atomic number of 48, which means it has 48 electrons. Its electron configuration can be written as: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10}\] Now, find the appropriate noble-gas abbreviation. Krypton (Kr) has an atomic number of 36 and sits right before Cd in the periodic table, with an electron configuration of: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\] Using the noble-gas core abbreviation for krypton, the condensed electron configuration for Cadmium is: \[[\mathrm{Kr}] 5s^2 4d^{10}\]

(e) U - Uranium

First, find the electron configuration of Uranium using a periodic table. Uranium has an atomic number of 92, which means it has 92 electrons. Its electron configuration can be written as: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2 5f^3 6d^1\] Now, find the appropriate noble-gas abbreviation. Radium (Rn) has an atomic number of 86 and sits right before U in the periodic table, with its electron configuration: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2\] Using the noble-gas core abbreviation for radium, the condensed electron configuration for Uranium is: \[[\mathrm{Rn}] 5f^3 6d^1 7s^2\]

(f) Pb - Lead

First, find the electron configuration of Lead using a periodic table. Lead has an atomic number of 82, which means it has 82 electrons. Its electron configuration can be written as: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^2\] Now, find the appropriate noble-gas abbreviation. Xenon (Xe) has an atomic number of 54 and its electron configuration is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6\] Using the noble-gas core abbreviation for xenon, the condensed electron configuration for Lead is: \[[\mathrm{Xe}] 6s^2 4f^{14} 5d^{10} 6p^2\]

Key concepts

noble-gas core

The noble-gas core is a concept used in writing electron configurations more efficiently, especially for elements with many electrons. A noble gas is chosen as a reference, because they have complete valence shells, which makes them stable and predictable. When writing the electron configuration of an element, you can use a noble-gas core by representing the electron configuration of the nearest preceding noble gas with its chemical symbol in square brackets.

• For example, for cesium (Cs), the noble gas xenon (Xe) is used as a core. Cs has an atomic number of 55, while Xe has an atomic number of 54. So, the first 54 electrons in Cs are the same as in Xe, and can be represented as \[\text{Xe}\].
• The remaining configuration is written after this noble-gas core abbreviation, such as \[\text{Xe}] 6s^1\], creating a concise way to express the electron configuration.

This approach not only simplifies the notation but highlights the valence electrons, which are crucial for understanding chemical behavior. This is applicable for all atoms across the periodic table following the noble gas prior to them.

periodic table

The periodic table is a powerful tool for understanding the chemical properties and electron configurations of elements. It organizes elements in order of increasing atomic number and aligns them in rows and columns based on recurring chemical properties. Each row, or period, indicates the filling of a new electron shell. As you move from left to right across a period, electrons are filled into the successive orbitals.

• The table consists of 18 groups, or columns, which often share similar valence electron configurations, leading to similar chemical properties within the group.
• Noble gases, found in Group 18, are particularly stable due to their filled outer electron shells.
• The position of an element can help predict its electron configuration. For instance, nickel (Ni), located in the 4th period and the 10th group of transition metals, fills its 3d and 4s orbitals, leading to the configuration \[\text{Ar}] 4s^2 3d^8\].

Thus, the periodic table not only serves as a map of elements but aids in determining likely electron configurations and chemical reactivity.

condensed electron configuration

Condensed electron configuration is a shorthand notation that employs the noble-gas core to simplify the full electron configuration of elements. This method allows us to focus on the electrons that reside outside of the noble-gas structure, typically those in the outermost shells that determine most chemical reactions.A complete electron configuration lists all occupied sublevels in order:

• Example: Uranium (U) has a full electron configuration of \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^6 6s^2 4f^{14} 5d^{10} 6p^6 7s^2 5f^3 6d^1\].
• Using the noble-gas core, this is condensed to \[\text{Rn}] 5f^3 6d^1 7s^2\], highlighting Uranium's valence electrons.

By using the noble-gas core, the condensed electron configuration provides a more manageable framework, especially for elements with a large number of electrons, emphasizing the most chemically reactive parts of the atom.

noble-gas abbreviation

A noble-gas abbreviation is a technique used in writing condensed electron configurations. Instead of listing all the electrons up to the period of the element, the symbol of the preceding noble gas is used in brackets to denote the configuration of those initial electrons, streamlining the representation of the atom's electronic structure.Here's how you can employ noble-gas abbreviations:

• Find the noble gas that comes before the element in question. For example, for selenium (Se), argon (Ar) is the noble gas preceding it.
• Use this noble gas in brackets to represent all the electrons in selenium up to that point, then continue writing the remaining electron configuration: \[\text{Ar}] 4s^2 3d^{10} 4p^4\].

This abbreviation method is especially useful in limiting the complexity of electron configurations for elements with many electrons, focusing on outer electrons critical for chemical properties and reactions.