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Chapter 2: Problem 12

(a) What electron subshell is being filled for the rare earth series of elements on the periodic table? (b) What electron subshell is being filled for the actinide series?

Short Answer

Expert verified
Answer: (a) In the rare earth series, the 4f subshell is being filled. (b) In the actinide series, the 5f subshell is being filled.

Step by step solution

01

Understanding the Periodic Table and Electron Configuration

Firstly, let's review what electron subshells are. The electron configuration of an atom depends on the distribution of its electrons across various energy levels and subshells. Each energy level consists of several subshells (designated as s, p, d, and f), which can hold a specific maximum number of electrons: 2 for s, 6 for p, 10 for d, and 14 for f. Now let's study the periodic table, specifically the rare earth series and actinide series, to determine which electron subshell is being filled. The rare earth series consists of the lanthanides and are located in the sixth period. The actinide series consists of the actinides and are located in the seventh period. Both series belong to the f-block in the periodic table.
02

Determine the Electron Subshell for the Rare Earth Series

The rare earth series consists of the lanthanide elements, which have atomic numbers ranging from 57 (Lanthanum) to 71 (Lutetium). Excluding the first two elements (Lanthanum and Cerium), the remaining elements in the lanthanides have their electron configurations following the pattern [Xe] 4f^(n-54) 5d^1 6s^2, where n is the atomic number of the element. The f subshell is being filled in this series, specifically the 4f subshell.
03

Determine the Electron Subshell for the Actinide Series

The actinide series consists of the actinide elements, which have atomic numbers ranging from 89 (Actinium) to 103 (Lawrencium). Excluding the first two elements (Actinium and Thorium), the remaining elements in the actinides have their electron configurations following the pattern [Rn] 5f^(n-88) 6d^(0-1) 7s^2, where n is the atomic number of the element. The f subshell is being filled in this series, specifically the 5f subshell.
04

Answer to (a) and (b)

To answer the given exercise, the electron subshell being filled for the following series of elements is: (a) The rare earth series: 4f subshell (b) The actinide series: 5f subshell

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Most popular questions from this chapter

Explain why hydrogen fluoride (HF) has a higher boiling temperature than hydrogen chloride (HCl) \(\left(19.4^{\circ} \mathrm{C}\right.\) vs. \(\left.-85^{\circ} \mathrm{C}\right)\), even though HF has a lower molecular weight.

Cite the difference between atomic mass and atomic weight.

The net potential energy \(E_{N}\) between two adjacent ions is sometimes represented by the expression $$ E_{N}=-\frac{C}{r}+D \exp \left(-\frac{r}{\rho}\right) $$ in which \(r\) is the interionic separation and \(C\), \(D\), and \(\rho\) are constants whose values depend on the specific material. (a) Derive an expression for the bonding energy \(E_{0}\) in terms of the equilibrium interionic separation \(r_{0}\) and the constants \(D\) and \(\rho\) using the following procedure: 1\. Differentiate \(E_{N}\) with respect to \(r\) and set the resulting expression equal to zero. 2\. Solve for \(C\) in terms of \(D, \rho\), and \(r_{0}\) - 3\. Determine the expression for \(E_{0}\) by substitution for \(C\) in Equation \(2.12\). (b) Derive another expression for \(E_{0}\) in terms of \(r_{0}, C\), and \(\rho\) using a procedure analogous to the one outlined in part (a).

(a) Cite two important quantum-mechanical concepts associated with the Bohr model of the atom. (b) Cite two important additional refinements that resulted from the wave- mechanical atomic model.

Give the electron configurations for the following ions: \(\mathrm{Fe}^{2+}, \mathrm{Al}^{3+}, \mathrm{Cu}^{+}, \mathrm{Ba}^{2+}, \mathrm{Br}^{-}\), and \(\mathrm{O}^{2-}\)
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