Ch.7 - Periodic Properties of the Elements

Problem 13

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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 𝑍eff? Which element or elements have the largest effective nuclear charge?

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Effective nuclear charge (Z_{eff}) is calculated using the formula: Z_{eff} = Z - S, where Z is the atomic number and S is the shielding constant.

To find the element with the smallest Z_{eff}, identify the element with the smallest atomic number (Z) and consider the shielding effect.

Hydrogen (Z=1) has the smallest atomic number among elements 1-18, and since it has no inner electrons, its shielding constant (S) is minimal, making its Z_{eff} the smallest.

To find the element with the largest Z_{eff}, identify the element with the largest atomic number (Z) and consider the shielding effect.

Argon (Z=18) has the largest atomic number among elements 1-18, and due to its filled electron shells, the effective nuclear charge experienced by its outer electrons is maximized, making its Z_{eff} the largest.

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Key Concepts

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

Effective Nuclear Charge (Z_eff)

Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the actual nuclear charge (number of protons) and the shielding effect caused by other electrons. Z_eff can be calculated using Slater's rules or other methods, and it helps explain trends in atomic size and ionization energy across the periodic table.

Shielding Effect

The shielding effect refers to the phenomenon where inner-shell electrons partially block the attraction between the nucleus and the outer-shell electrons. This results in a lower effective nuclear charge felt by the outer electrons. Understanding the shielding effect is crucial for predicting how atomic properties change across periods and groups in the periodic table.

Periodic Trends

Periodic trends are patterns observed in the properties of elements as you move across a period or down a group in the periodic table. Key trends include atomic radius, ionization energy, and electronegativity, which are influenced by effective nuclear charge and shielding. Recognizing these trends helps in predicting the behavior of elements and their reactivity.

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Periodic Trends

Related Practice

The graph below shows the ionization energies for a particular element. In which group is the element most likely a member of? [Section 7.3]

Textbook Question

Group 1A and 2A elements are sometimes called, collectively, “the s-block.” Therefore, what is an analogous name for the entire collection of the group 3A, 4A, 5A, 6A, 7A, and 8A elements?

Textbook Question

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?

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 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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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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