Problem 102 - Chemistry Matter and Change

Question

Which element has the ground-state electron configuration represented by the noble-gas notation \([\mathrm{Rn}] 7 \mathrm{s}^{1} ?\)

Step-by-Step Solution

Answer

The element that has the ground-state electron configuration represented by the noble-gas notation \([\mathrm{Rn}] 7 \mathrm{s}^{1}\) is Francium (Fr).

Step 1: Identify the noble gas with a core electron configuration

First, let's determine the electron configuration of the noble gas Rn (Radon). Radon is in period 6, group 18, and has an atomic number of 86. The electron configuration of Radon is: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶6s²4f¹⁴5d¹⁰6p⁶ Now that we have the electron configuration for Radon, we can move on to determine the element with the given electron configuration.

Step 2: Identify the element with the given electron configuration

The given electron configuration is [Rn]7s¹. Since we've already found Radon's electron configuration, we can replace [Rn] with its electron configuration to obtain the complete electron configuration for the element in question: 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶6s²4f¹⁴5d¹⁰6p⁶7s¹ Now let's find the element with this electron configuration. We will follow the order of filling the orbitals based on the Aufbau principle: 1s²(2) → 2s²(4) → 2p⁶(10) → 3s²(12) → 3p⁶(18) → 4s²(20) → 3d¹⁰(30) → 4p⁶(36) → 5s²(38) → 4d¹⁰(48) → 5p⁶(54) → 6s²(56) → 4f¹⁴(70) → 5d¹⁰(80) → 6p⁶(86) → 7s¹(87) The element has A atomic number of 87, which corresponds to Francium (Fr).

Step 3: Conclusion

The element that has the ground-state electron configuration represented by the noble-gas notation [Rn]7s¹ is Francium (Fr).

Key Concepts

Noble-Gas Notation

Noble-gas notation is a helpful method to simplify electron configurations. Instead of writing out the full electron configuration, you use the closest noble gas with a lower atomic number as a reference.
This approach shortens the notation, saving time and effort, especially for elements with many electrons. For example, in the exercise, Radon ( [ ext{Rn}] ) is the noble gas used to abbreviate the electron configuration for Francium.

• Noble gases are located in Group 18 of the periodic table.
• They are known for their stable electron configurations, which makes them ideal references.
• This notation only changes the visualization; it doesn't affect the electron structure itself.

Using noble-gas notation not only makes writing and reading electron configurations easier, but it also emphasizes the orderly nature of the periodic table.

Aufbau Principle

The Aufbau Principle is a rule guiding the order in which electrons fill atomic orbitals. It states that electrons occupy the lowest energy level first before moving to higher levels. This orderly filling is dictated by a sequence of increasing energy, preventing chaos in electron orientations.

• Electrons fill according to increasing orbital energies: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s.
• The principle also helps predict ground-state electron configurations, as it was used in the solution to determine Francium's electron configuration.
• It aligns with the periodic table's structure, as observed with blocks corresponding to s, p, d, and f subshells.

This principle is essential in understanding why each element exhibits its distinct chemical properties.

Ground-State Electron Configuration

Ground-state electron configuration describes how electrons are arranged in an atom's shells and subshells when the atom is in its lowest energy state. It's fundamental for predicting an element's chemical behavior.
The configuration reveals not just where electrons reside, but also the energy dynamics of atoms.

• The notation uses numbers and letters to designate specific energy levels and orbitals, like in [ ext{Rn}]7s¹ for Francium. "7" represents the energy level, and "s" indicates the type of subshell.
• Ground-state configurations help to identify the number of valence electrons, which is crucial for chemical reactions.
• The concept also integrates features of the Aufbau principle since electrons aim to occupy the lowest energy states available.

Understanding ground-state configurations is key for insights into an element's reactivity and placement on the periodic table.

Periodic Table

The periodic table is a comprehensive chart organizing all known elements by increasing atomic number. It's a pivotal tool in chemistry for understanding electron configurations and predicting chemical behavior.
Elements are arranged so that those with similar properties fall into the same groups or columns.

• The table is divided into periods (rows) and groups (columns).
• It effectively demonstrates periodic trends, including electron affinities, atomic sizes, and electronegativity.
• The organization reflects electron configurations, as seen in the placement of Francium right below Cesium in group 1, like their shared single electron in the outermost s-orbital.

The periodic table is much more than just an element list; it's a map of the building blocks that gives insight into the forces of nature.