Ch.7 - Periodic Properties of the Elements

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.7 - Periodic Properties of the Elements

문제 15b

7장, 문제 15b

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?

검증된 단계별 안내

Identify the electron configuration for each element: Sodium (Na) has an electron configuration of 1s² 2s² 2p⁶ 3s¹, and Potassium (K) has an electron configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹.

Apply Slater's rules to determine the shielding constant (S) for the outermost electron in each atom. For Na, the 3s electron is shielded by the 1s, 2s, and 2p electrons. For K, the 4s electron is shielded by the 1s, 2s, 2p, 3s, and 3p electrons.

Calculate the shielding constant (S) for Na: According to Slater's rules, electrons in the same group (n-1) contribute 0.85 each, and electrons in lower groups contribute 1.00 each. Calculate S for Na using these contributions.

Calculate the shielding constant (S) for K: Similarly, apply Slater's rules to calculate S for K, considering the contributions from the electrons in the same and lower groups.

Estimate the effective nuclear charge (Zeff) using the formula Zeff = Z - S, where Z is the atomic number. Calculate Zeff for both Na and K using the shielding constants obtained from Slater's rules.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Effective Nuclear Charge (Zeff)

Effective Nuclear Charge (Zeff) refers to the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect of inner electrons, which reduces the full nuclear charge felt by outer electrons. Understanding Zeff is crucial for predicting atomic properties such as ionization energy and atomic size.

Slater's Rules

Slater's Rules provide a systematic method for estimating the effective nuclear charge experienced by an electron in an atom. The rules involve assigning different shielding contributions based on the electron's group and principal quantum number, allowing for a more accurate calculation of Zeff. This method is particularly useful for comparing Zeff across different elements.

Shielding Effect

The shielding effect occurs when inner-shell electrons partially block the attractive force of the nucleus on outer-shell electrons. This results in a lower effective nuclear charge for the outer electrons, influencing their energy levels and reactivity. Understanding the shielding effect is essential for interpreting trends in atomic and ionic properties across the periodic table.

관련 실천

교과서 질문

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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교과서 질문

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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교과서 질문

Among the elements N, O, P, and S, which element or elements have the smallest effect 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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교과서 질문

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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교과서 질문

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?