Problem 8 - Chemistry and Chemical Reactivity

Question

The lanthanides, once called the rare earth elements, are really only "medium rare." Using noble gas and spdf notations, depict reasonable electron configurations for the following elements. (a) Samarium, Sm. This lanthanide is used in magnetic materials. (b) Ytterbium, Yb. This element was named for the village of Ytterby in Sweden, where a mineral source of the element was found.

Step-by-Step Solution

Answer

Sm: [Xe] 4f^6 6s^2; Yb: [Xe] 4f^{14} 6s^2.

Step 1: Understand the Electron Configuration Sequence

The electron configuration of an atom follows the order of filling of electron orbitals as per the Aufbau principle. For elements, the filling order is typically described as 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

Step 2: Writing Electron Configuration for Samarium (Sm)

Samarium (Sm) has an atomic number of 62. Therefore, it has 62 electrons. The electron configuration in noble gas notation is organized by using Xenon (Xe), the closest noble gas with a higher atomic number, as a reference. "[Xe] 4f^6 6s^2" represents Samarium's electron configuration because Samarium fills up to the 4th f-orbital (4f) and continues with the 6s orbital.

Step 3: Confirming the Electron Configuration of Samarium

Ensure that all 62 electrons are accounted for. Xenon configuration represents 54 electrons. Adding 4f^6 (6 electrons) and 6s^2 (2 electrons) gives a total of 62. Therefore, Sm: [Xe] 4f^6 6s^2.

Step 4: Writing Electron Configuration for Ytterbium (Yb)

Ytterbium (Yb) has an atomic number of 70. Therefore, it has 70 electrons. Similar to Samarium, we use Xenon (Xe) as the reference point for electron configuration notation. "[Xe] 4f^{14} 6s^2" represents Ytterbium's electron configuration because Ytterbium completes filling the 4f orbital and fills the 6s orbital.

Step 5: Confirming the Electron Configuration of Ytterbium

Verify that all 70 electrons are used. The Xenon configuration represents 54 electrons. Adding 4f^{14} (14 electrons) and 6s^2 (2 electrons) confirms that Yb: [Xe] 4f^{14} 6s^2 represents 70 electrons.

Key Concepts

Electron Configuration

Electron configuration is a way of arranging the electrons in an atom's electron shell. It describes the distribution of electrons among the atomic orbitals. Each electron in an atom occupies a specific orbital, and they fill from lower to higher energy levels. This order is dictated by the principles of quantum mechanics. The electrons fill orbitals in a specific sequence based on energy levels and the electron's sublevels, such as s, p, d, and f.

• s-orbitals can hold up to 2 electrons.
• p-orbitals can accommodate up to 6 electrons.
• d-orbitals can contain up to 10 electrons.
• f-orbitals can hold up to 14 electrons.

Knowing the electron configuration of an element helps in understanding its chemical properties and behavior, including reactivity and bonding patterns.

Aufbau Principle

The Aufbau Principle is a rule used to determine the electron configuration of atoms. According to this principle, electrons occupy the lowest energy orbitals available. This process of "building up" the electron configuration is systematic, beginning with the 1s orbital and moving outward through increasing energy levels and sublevels. The sequence in which these orbitals fill is given by the order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, and so on. It's important to remember that for some transition metals and inner transition metals like the lanthanides, the d and f sublevels play a critical role. They can result in deviations from the straightforward Aufbau order due to their close energy proximities.

Noble Gas Notation

Noble gas notation is a shorthand version of writing an element's electron configuration. It uses the electron configuration of the nearest preceding noble gas to simplify the notation. For example, rather than writing the entire configuration for Samarium (Sm) or Ytterbium (Yb), use Xenon (Xe) with the configuration [Xe] as a reference.

• [Xe] 4f⁶ 6s² for Samarium
• [Xe] 4f¹⁴ 6s² for Ytterbium

This abbreviation allows us to quickly understand the outer electron structure without recounting the inner electrons. It simplifies calculations and helps in predicting the element's chemical properties and behavior.

Samarium

Samarium is one of the lanthanide elements, characterized by its use in various magnetic materials, batteries, and some cancer treatment drugs. Placed on the periodic table with an atomic number of 62, samarium's electron configuration can be studied with a noble gas notation. Starting from Xenon's electron configuration, add on the electrons correlated with Samarium: - (54 electrons from Xe) - Plus 4f⁶ (6 additional electrons) - And 6s² (2 more electrons) This leads to the complete notation for samarium: [Xe] 4f⁶ 6s². This notation identifies samarium's reactivity and its significance in forming magnetic materials.

Ytterbium

Ytterbium is another member of the lanthanide series. It bears the atomic number 70 and is notable for its applications in improving stainless steel properties and in some lasers. The electron configuration of ytterbium can also be represented using noble gas notation. With Xenon as a reference, ytterbium's configuration expands with: - (54 electrons from Xe) - 4f¹⁴ (14 added electrons) - 6s² (2 additional electrons) This culminates in the noble gas notation: [Xe] 4f¹⁴ 6s². Through this configuration, we understand its tendency to be less reactive, trending towards full sublevel completion, crucial for its role in innovative technologies.