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Chapter 7: Problem 13

Among elements 1-18, which element or elements have the smallest effective nuclear charge if we use Equation 7.1 to calculate \(Z_{\text { eff}}\)? Which element or elements have the largest effective nuclear charge?

Short Answer

Expert verified
After calculating the effective nuclear charge (\(Z_{\text { eff }}\)) for elements 1-18 using the equation \(Z_{\text { eff }} = Z - S\), where Z is the atomic number and S is the shielding constant, we can determine the element(s) with the smallest and largest effective nuclear charge by comparing the calculated values. The element(s) with the smallest \(Z_{\text { eff }}\) value will have the smallest effective nuclear charge, while the element(s) with the largest \(Z_{\text { eff }}\) value will have the largest effective nuclear charge.

Step by step solution

01

Write Electron Configurations for Elements 1-18

Write the electron configurations for elements 1-18 considering their atomic numbers. Knowing the electron configurations will enable us to determine the shielding constant for each element.
02

Calculate the Shielding Constant (S) for Each Element

For each element, determine the shielding constant (S) based on the electron configuration. Consider following rules for calculation: 1. Electrons in the same subshell shield each other by approximately 0.35. 2. Electrons in the immediate preceding shell shield by approximately 0.85. 3. Electrons in shells two or more before the outermost shell have full shielding effect of 1.
03

Calculate the Effective Nuclear Charge (Z_eff) for Each Element using Equation 7.1

For each element, apply the equation: \(Z_{\text{eff}} = Z - S\) where Z is the atomic number (number of protons) and S is the calculated shielding constant. Calculate the effective nuclear charge (Z_eff) for each element from 1-18.
04

Identify the Elements with the Smallest and Largest Effective Nuclear Charges

Compare the calculated Z_eff values for all elements 1-18, and determine the elements with the smallest and largest effective nuclear charges. The element(s) with the smallest Z_eff value will have the smallest effective nuclear charge, and the element(s) with the largest Z_eff value will have the largest effective nuclear charge.

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Most popular questions from this chapter

(a) As described in Section 7.7 , the alkali metals react with hydrogen to form hydrides and react with halogens to form halides. Compare the roles of hydrogen and halogens in these reactions. Write balanced equations for the reaction of fluorine with calcium and for the reaction of hydrogen with calcium. (b) What is the oxidation number and electron configuration of calcium in each product?

Arrange each of the following sets of atoms and ions, in order of increasing size: \((\mathbf{a}) \mathrm{Se}^{2-}, \mathrm{Te}^{2-}, \mathrm{Se} ;(\mathbf{b}) \mathrm{Co}^{3+}, \mathrm{Fe}^{2+}, \mathrm{Fe}^{3+};\) \((\mathbf{c}) \mathrm{Ca}, \mathrm{Ti}^{4+}, \mathrm{Sc}^{3+} ;(\mathbf{d}) \mathrm{Be}^{2+}, \mathrm{Na}^{+}, \mathrm{Ne}.\)

(a) Does metallic character increase, decrease, or remain unchanged as one goes from left to right across a row of the periodic table? (b) Does metallic character increase, decrease, or remain unchanged as one goes down a column of the periodic table? (c) Are the periodic trends in (a) and (b) the same as or different from those for first ionization energy?

The following observations are made about two hypothetical elements \(A\) and \(B :\) The \(A-A\) and \(B-B\) bond lengths in the elemental forms of \(A\) and \(B\) are 2.36 and \(1.94 \hat{A},\) respectively. A and \(\mathrm{B}\) react to form the binary compound \(\mathrm{AB}_{2},\) which has a linear structure (that is \(\angle \mathrm{B}-\mathrm{A}-\mathrm{B}=180^{\circ} ) .\) Based on these statements, predict the separation between the two B nuclei in a molecule of \(\mathrm{AB}_{2}\) .

As we move across a period of the periodic table, why do the sizes of the transition elements change more gradually than those of the representative elements?
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