Problem 69 - Chemistry The Central Science

Question

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

Step-by-Step Solution

Answer

The condensed electron configurations using noble-gas core abbreviations for the given atoms are as follows: a) Cs: [\(Xe\)]6s¹ b) Ni: [\(Ar\)]4s²3d⁸ c) Se: [\(Ar\)]4s²3d¹⁰4p⁴ d) Cd: [\(Kr\)]5s²4d¹⁰ e) U: [\(Rn\)]7s²5f³ f) Pb: [\(Xe\)]6s²4f¹⁴5d¹⁰6p²

Step 1: Identify the nearest noble gas with fewer electrons

For each element, find the noble gas with fewer electrons and atomic number closest to the given atom. Write down their element symbols and atomic numbers for reference. a) Cs (Cesium): Xe, 54 b) Ni (Nickel): Ar, 18 c) Se (Selenium): Ar, 18 d) Cd (Cadmium): Kr, 36 e) U (Uranium): Rn, 86 f) Pb (Lead): Xe, 54

Step 2: Write the electron configuration from the noble gas core to the atom

Write the electron configuration from the atomic number of the noble gas core to the atomic number of the given atom. Use the periodic table to aid you in identifying the orbitals being filled. a) Cs: \(Xe\) -> 6s¹ b) Ni: \(Ar\) -> 4s²3d⁸ c) Se: \(Ar\) -> 4s²3d¹⁰4p⁴ d) Cd: \(Kr\) -> 5s²4d¹⁰ e) U: \(Rn\) -> 7s²5f³ f) Pb: \(Xe\) -> 6s²4f¹⁴5d¹⁰6p²

Step 3: Combine the noble gas core abbreviation with the electron configurations

Replace the noble gas symbols with their electron configuration abbreviations in brackets and combine them with the electron configurations found in Step 2. a) Cs: [\(Xe\)]6s¹ b) Ni: [\(Ar\)]4s²3d⁸ c) Se: [\(Ar\)]4s²3d¹⁰4p⁴ d) Cd: [\(Kr\)]5s²4d¹⁰ e) U: [\(Rn\)]7s²5f³ f) Pb: [\(Xe\)]6s²4f¹⁴5d¹⁰6p²

Key Concepts

Noble Gas Core Abbreviation

The noble gas core abbreviation is a useful shorthand technique in writing electron configurations for elements. This approach involves using the electron configuration of a noble gas that comes right before the element in question, thereby simplifying the notation.
For example, rather than listing out the entire electron configuration from the first orbitals, you use the symbol of the nearest noble gas enclosed in square brackets to represent all the filled orbitals up to that noble gas.
Let's take Nickel (Ni) as an example:
- First, identify the noble gas preceding Nickel on the periodic table, which is Argon (Ar) with an atomic number of 18.
- So, the electron configuration of Nickel can start with [Ar], indicating that those inner-shell electrons are identical to Argon's.
The next step involves writing out the remaining electrons beyond Argon. Thus, the electron configuration for Nickel becomes [Ar]4s²3d⁸. In this way, the condensed notation quickly conveys necessary information without overwhelming detail.
By using noble gas symbols in electron configurations, chemists save space and time while ensuring clarity.

Periodic Table

The periodic table is an essential tool in chemistry, acting as a comprehensive map of all known elements, including metals, nonmetals, and metalloids. Each element is placed in a unique position based on its atomic number, which denotes the number of protons in its nucleus.
The table is divided into rows, known as periods, and columns known as groups or families. Elements in the same group often share chemical properties, as they have the same number of electrons in their outer shell.
Using the periodic table to write electron configurations involves understanding the overall layout:
- **Periods (Rows):** Elements are arranged in increasing atomic number from left to right. Moving through a period fills successive electron shells.
- **Groups (Columns):** Vertical columns represent elements that typically have similar valence electron configurations. For instance, the noble gases, like Argon (Ar), Krypton (Kr), and Xenon (Xe) are all found in the same group because of their filled outer electron shells.
Utilizing this structure, you can efficiently locate the nearest noble gas to start your electron configuration. For example, if you are finding the configuration for Selenium (Se), which has an atomic number of 34, its nearest noble gas is Argon (Ar), with an atomic number of 18.
The periodic table also shows the order of orbital filling, guiding you to determine which orbitals are occupied in their sequence.

Electron Configuration Steps

Following a structured process to determine electron configurations allows you to correctly and efficiently assign electrons to an atom's orbitals. Here's a simple guide broken down into steps:
1. **Identify the Nearest Noble Gas:** Look at the periodic table and find the noble gas that comes just before your element of interest. Use this as your starting point.
2. **Count the Electrons Beyond the Noble Gas:** Subtract the atomic number of the noble gas from your element's atomic number. This gives you the number of additional electrons to consider. 3. **Determine Orbital Filling Order:** Use the layout of the periodic table and the Aufbau principle to fill orbitals from lowest to highest energy: following the sequence 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, etc.
4. **Write the Configuration:** Begin with the noble gas core abbreviation (e.g., [Ar]), then add the remaining orbitals until you've accounted for all the element's electrons.
For example, by methodically following these steps, the configuration for Cadmium (Cd), with an atomic number of 48, uses [Kr] as the noble gas core followed by the next orbitals to get [Kr]5s²4d¹⁰.
Through practice, these steps become second nature, empowering you to tackle diverse electron shells efficiently.