Ch.7 - Periodic Properties of the Elements

Problem 15e

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Chapter 7, Problem 15e

Detailed calculations show that the value of Zeff for the outermost electrons in Na and K atoms is 2.51+ and 3.49+, respectively. (e) Predict Zeff for the outermost electrons in the Rb atom based on the calculations for Na and K.

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Understand the concept of effective nuclear charge (Z_{eff}): It is the net positive charge experienced by an electron in a multi-electron atom.

Recognize the trend in Z_{eff} across the alkali metals (Na, K, Rb): As you move down a group in the periodic table, the Z_{eff} generally increases due to the addition of more protons in the nucleus.

Note the given Z_{eff} values for Na and K: Na has a Z_{eff} of 2.51+ and K has a Z_{eff} of 3.49+.

Predict the Z_{eff} for Rb: Since Rb is below K in the periodic table, its Z_{eff} should be slightly higher than that of K, following the trend.

Estimate the Z_{eff} for Rb by considering the incremental increase from Na to K and applying a similar increase from K to Rb.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Effective Nuclear Charge (Zeff)

Effective Nuclear Charge (Zeff) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the actual nuclear charge (the number of protons) and the shielding effect caused by inner-shell electrons. As the number of protons increases, the Zeff typically increases, leading to stronger attraction between the nucleus and the outermost electrons.

Shielding Effect

The shielding effect refers to the phenomenon where inner-shell electrons partially block the attraction between the nucleus and the outermost electrons. This results in a lower effective nuclear charge felt by the outer electrons. The greater the number of inner electrons, the more significant the shielding effect, which influences the Zeff value for outer electrons in larger atoms.

Trends in Zeff Across Periods

Zeff generally increases across a period in the periodic table due to the increase in nuclear charge without a corresponding increase in shielding. However, as you move down a group, the addition of electron shells increases shielding, which can lead to a smaller increase in Zeff. Understanding these trends helps predict Zeff values for elements based on their position in the periodic table.

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Periodic Trends

Related Practice

The prefix eka- comes from the Sanskrit word for 'one.' Mendeleev used this prefix to indicate that the unknown element was one place away from the known element that followed the prefix. For example, eka-silicon, which we now call germanium, is one element below silicon. Mendeleev also predicted the existence of eka-manganese, which was not experimentally confirmed until 1937 because this element is radioactive and does not occur in nature. Based on the periodic table shown in Figure 7.1, what do we now call the element Mendeleev called eka-manganese?

Among elements 1–18, which element or elements have the smallest effective nuclear charge if we use Equation 7.1 to calculate 𝑍eff? Which element or elements have the largest effective nuclear charge?

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Textbook Question

Which of the following statements about effective nuclear charge for the outermost valence electron of an atom is incorrect? (i) The effective nuclear charge can be thought of as the true nuclear charge minus a screening constant due to the other electrons in the atom. (ii) Effective nuclear charge increases going left to right across a row of the periodic table. (iii) Valence electrons screen the nuclear charge more effectively than do core electrons. (iv) The effective nuclear charge shows a sudden decrease when we go from the end of one row to the beginning of the next row of the periodic table. (v) The change in effective nuclear charge going down a column of the periodic table is generally less than that going across a row of the periodic table

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Textbook Question

Detailed calculations show that the value of Zeff for the outermost electrons in Si and Cl atoms is 4.29+ and 6.12+, respectively. (a) What value do you estimate for Zeff experienced by the outermost electron in both Si and Cl by assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant?

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Textbook Question

Which will experience the greater effective nuclear charge, the electrons in the 𝑛=3 shell in Ar or the 𝑛=3 shell in Kr? Which is more likely to be closer to the nucleus?

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Textbook Question

Arrange the following atoms in order of increasing effective nuclear charge experienced by the electrons in the 𝑛=3 electron shell: K, Mg, P, Rh, Ti.

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