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Chapter 2: Problem 11

Without consulting Figure 2.6 or Table \(2.2,\) determine whether each of the electron configurations given below 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) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\)

Short Answer

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Question: Identify the family of each element based on its electron configuration. (a) 1s虏 2s虏 2p鈦� 3s虏 3p鈦� (b) 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 3d鈦� 4s虏 (c) 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 3d鹿鈦� 4s虏 4p鈦� (d) 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s鹿 (e) 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 3d鹿鈦� 4s虏 4p鈦� 4d鈦� 5s虏 (f) 1s虏 2s虏 2p鈦� 3s虏

Step by step solution

01

(a) Electron Configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦�

The outermost shell is the third shell, which has 7 electrons (3s虏 3p鈦�). Since this lacks one electron to achieve a full outer shell, the element is a halogen.
02

(b) Electron Configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 3d鈦� 4s虏

The outermost shell is the fourth shell, which has 2 electrons (4s虏). Additionally, the element has a partially filled d subshell (3d鈦�). This makes it a transition metal.
03

(c) Electron Configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 3d鹿鈦� 4s虏 4p鈦�

The outermost shell is the fourth shell, and it has 8 electrons (4s虏 4p鈦�). Since the outer shell is full, the element is an inert gas.
04

(d) Electron Configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 4s鹿

The outermost shell is the fourth shell, which has 1 electron (4s鹿). Since there is only one valence electron, the element is an alkali metal.
05

(e) Electron Configuration: 1s虏 2s虏 2p鈦� 3s虏 3p鈦� 3d鹿鈦� 4s虏 4p鈦� 4d鈦� 5s虏

The outermost shell is the fifth shell, which has 2 electrons (5s虏). Additionally, the element has a partially filled d-subshell (4d鈦�). This makes it a transition metal.
06

(f) Electron Configuration: 1s虏 2s虏 2p鈦� 3s虏

The outermost shell is the third shell, which has 2 electrons (3s虏). Since there are two valence electrons, the element is an alkaline earth metal.

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Most popular questions from this chapter

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

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).

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

The net potential energy between two adjacent ions, \(E_{N}\), may be represented by the sum of Equations \(2.8\) and \(2.9\); that is, $$ E_{N}=-\frac{A}{r}+\frac{B}{r^{n}} $$ Calculate the bonding energy \(E_{0}\) in terms of the parameters \(A, B\), and \(n\) using the following procedure: 1\. Differentiate \(E_{N}\) with respect to \(r\), and then set the resulting expression equal to zero, because the curve of \(E_{N}\) versus \(r\) is a minimum at \(E_{0 \text { - }}\) 2\. Solve for \(r\) in terms of \(A, B\), and \(n\), which yields \(r_{0}\), the equilibrium interionic spacing. 3\. Determine the expression for \(E_{0}\) by substituting \(r_{0}\) into Equation \(2.11\).

6 Allowed values for the quantum numbers of electrons are as follows: $$ \begin{aligned} n &=1,2,3, \ldots \\ l &=0,1,2,3, \ldots, n-1 \\ m_{l} &=0, \pm 1, \pm 2, \pm 3, \ldots, \pm l \\ m_{s} &=\pm \frac{1}{2} \end{aligned} $$ The relationships between \(n\) and the shell designations are noted in Table 2.1. Relative to the subshells, \(l=0\) corresponds to an \(s\) subshell \(l=1\) corresponds to a \(p\) subshell \(l=2\) corresponds to a \(d\) subshell \(l=3\) corresponds to an \(f\) subshell For the \(K\) shell, the four quantum numbers for each of the two electrons in the \(1 s\) state, in the order of \(n l m_{i} m_{s}\), are \(100 \frac{1}{2}\) and \(100\left(-\frac{1}{2}\right)\) Write the four quantum numbers for all of the electrons in the \(L\) and \(M\) shells, and note which correspond to the \(s, p\), and \(d\) subshells.
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