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Chapter 2: Problem 14

(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) For the rare earth series, the electron subshell being filled is the 4f subshell. (b) For the actinide series, the electron subshell being filled is the 5f subshell.

Step by step solution

01

Understanding electron subshells

Electron subshells are specific areas within an atom's electron shells where electrons with the same energy level are likely to be found. They are designated by the principal quantum number (n), which indicates the energy level of the electron, and the azimuthal quantum number (l), which specifies the shape of the orbital. The different subshells are represented by the letters s, p, d, and f, which correspond to l values of 0, 1, 2, and 3, respectively.
02

Identifying the rare earth series

The rare earth series consists of elements with atomic numbers 57 through 71, which includes elements like Lanthanum (La), Cerium (Ce), and Dysprosium (Dy). These elements are part of the larger group known as the Lanthanides and are located in the f-block of the periodic table.
03

Identifying the electron subshell being filled for the rare earth series

Since the rare earth series elements are in the f-block of the periodic table, it indicates that the electron subshells being filled for these elements are the f-subshells. More specifically, the underlying electron configuration for the Lanthanides is [Xe] 4f^n 5d^0-1 6s^2, where Xe represents the electron configuration of Xenon and n varies from 1 to 14 for the 14 elements in the series. So, for the rare earth series, the electron subshell being filled is the 4f subshell.
04

Identifying the actinide series

The actinide series consists of elements with atomic numbers 89 through 103, which includes elements like Actinium (Ac), Uranium (U), and Plutonium (Pu). These elements are part of the larger group known as the Actinides and are also located in the f-block of the periodic table.
05

Identifying the electron subshell being filled for the actinide series

Since the actinide series elements are also in the f-block of the periodic table, it indicates that the electron subshells being filled for these elements are the f-subshells as well. More specifically, the underlying electron configuration for the Actinides is [Rn] 5f^n 6d^0-1 7s^2, where Rn represents the electron configuration of Radon and n varies from 1 to 14 for the 14 elements in the series. So, for the actinide series, the electron subshell being filled is the 5f subshell. Answers: (a) For the rare earth series, the electron subshell being filled is the 4f subshell. (b) For the actinide series, the electron subshell being filled is the 5f subshell.

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Most popular questions from this chapter

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: (i) Differentiate \(E_{N}\) with respect to \(r\), and set the resulting expression equal to zero. (ii) Solve for \(C\) in terms of \(D, \rho\), and \(r_{0}\). (iii) Determine the expression for \(E_{0}\) by substitution for \(C\) in Equation \(2.18\). (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).

Relative to electrons and electron states, what does each of the four quantum numbers specify?

For an \(\mathrm{Na}^{+}-\mathrm{Cl}^{-}\)ion pair, attractive and repulsive energies \(E_{A}\) and \(E_{R}\), respectively, depend on the distance between the ions \(r\), according to $$ \begin{aligned} &E_{A}=-\frac{1.436}{r} \\ &E_{R}=\frac{7.32 \times 10^{-6}}{r^{8}} \end{aligned} $$ For these expressions, energies are expressed in electron volts per \(\mathrm{Na}^{+}-\mathrm{Cl}^{-}\)pair, and \(r\) is the distance in nanometers. The net energy \(E_{N}\) is just the sum of the preceding two expressions. (a) Superimpose on a single plot \(E_{N}, E_{R}\), and \(E_{A}\) versus \(r\) up to \(1.0 \mathrm{~nm}\). (b) On the basis of this plot, determine (i) the equilibrium spacing \(r_{0}\) between the \(\mathrm{Na}^{+}\)and \(\mathrm{Cl}^{-}\) ions, and (ii) the magnitude of the bonding energy \(E_{0}\) between the two ions. (c) Mathematically determine the \(r_{0}\) and \(E_{0}\) values using the solutions to Problem 2.18, and compare these with the graphical results from part (b).

Without consulting Figure \(2.8\) or Table \(2.2\), determine whether each of the following electron configurations is an inert gas, a halogen, an alkali metal, an alkaline earth metal, or a transition metal. Justify your choices. (a) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{5}\) (b) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{7} 4 s^{2}\) (c) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6}\) (d) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{1}\) (e) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6} 4 d^{5} 5 s^{2}\) (f) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\)

The atomic radii of \(\mathrm{Mg}^{2+}\) and \(\mathrm{F}^{-}\)ions are \(0.072\) and \(0.133 \mathrm{~nm}\), respectively. (a) Calculate the force of attraction between these two ions at their equilibrium interionic separation (i.e., when the ions just touch one another). (b) What is the force of repulsion at this same separation distance?
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