Detailed calculations show that the value of Zeff for the outermost electrons in Na and K atoms is 2.51+ and 3.49+, respectively. (a) What value do you estimate for Zeff experienced by the outermost electron in both Na and K by assuming core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant?

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Identify the atomic numbers of sodium (Na) and potassium (K). Sodium has an atomic number of 11, and potassium has an atomic number of 19.

Determine the number of core electrons for each element. For Na, the core electrons are the 1s, 2s, and 2p electrons, totaling 10. For K, the core electrons are the 1s, 2s, 2p, 3s, and 3p electrons, totaling 18.

Apply the formula for effective nuclear charge (Z_eff): Z_eff = Z - S, where Z is the atomic number and S is the screening constant. The screening constant S is calculated by assuming each core electron contributes 1.00 and each valence electron contributes 0.00.

Calculate the screening constant S for Na: S = 10 (since there are 10 core electrons). For K: S = 18 (since there are 18 core electrons).

Estimate Z_eff for Na and K using the formula: For Na, Z_eff = 11 - 10. For K, Z_eff = 19 - 18.

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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 other electrons. The greater the Zeff, the stronger the attraction between the nucleus and the outermost electrons, influencing atomic size and ionization energy.

Shielding Effect

The shielding effect refers to the phenomenon where inner electrons partially block the attraction between the nucleus and the outermost electrons. This results in a lower effective nuclear charge felt by the valence electrons. In calculations, core electrons are often assigned a specific contribution to the screening constant, which helps estimate the Zeff for outer electrons.

Valence and Core Electrons

Electrons in an atom are categorized as valence or core electrons. Valence electrons are those in the outermost shell and are involved in chemical bonding, while core electrons are located in inner shells and do not participate in bonding. Understanding the distinction between these two types of electrons is crucial for calculating Zeff, as they contribute differently to the shielding effect.

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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 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

Among the elements N, O, P, and S, which element or elementshave the smallest effect nuclear charge if we use Equation7.1 to calculate Zeff? Which element or elements havethe largest effective nuclear charge?

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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. (b) What values do you estimate for Zeff using Slater’s rules?