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Ch.7 - Periodic Properties of the Elements
All textbooksBrown 14th EditionCh.7 - Periodic Properties of the ElementsProblem 16
Chapter 7, Problem 16

Detailed calculations show that the value of Zeff for the outermost electrons in Si and Cl atoms is 4.29+ and 6.12+, respectively. (b) What values do you estimate for Zeff using Slater’s rules? (c) Which approach gives a more accurate estimate of Zeff? (d) Which method of approximation more accurately accounts for the steady increase in Zeff that occurs upon moving left to right across a period? (e) Predict Zeff for a valence electron in P (phosphorus) based on the calculations for Si and Cl.

Verified step by step guidance
1
To estimate Zeff using Slater's rules, first identify the electron configuration of the element. For Si (Silicon), the electron configuration is 1s² 2s² 2p⁶ 3s² 3p². For Cl (Chlorine), it is 1s² 2s² 2p⁶ 3s² 3p⁵.
Apply Slater's rules to calculate the shielding constant (S) for each element. For an electron in the 3p orbital, consider the contributions from electrons in the same group, the n-1 group, and the n-2 or lower groups. Use the specific Slater's rules coefficients for each group.
Calculate the effective nuclear charge (Zeff) using the formula: Zeff = Z - S, where Z is the atomic number of the element and S is the shielding constant calculated using Slater's rules.
Compare the Zeff values obtained using Slater's rules with the given detailed calculations. Discuss which method provides a more accurate estimate and why. Consider factors such as the assumptions made in Slater's rules and the empirical nature of the detailed calculations.
To predict Zeff for a valence electron in P (Phosphorus), use the trend observed in the Zeff values for Si and Cl. Consider the periodic trend of increasing Zeff across a period and interpolate or extrapolate based on the known values for Si and Cl.

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 minus the shielding effect of other electrons. This concept is crucial for understanding how strongly an electron is attracted to the nucleus, influencing atomic size, ionization energy, and electron affinity.
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Effective Nuclear Charge

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 assign different shielding contributions based on the electron's group and principal quantum number, allowing for a more refined calculation of Zeff. This method helps in comparing the shielding effects of different electron configurations.
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Effective Nuclear Charge Calculation with Slater's Rules

Trends in Zeff Across a Period

As you move from left to right across a period in the periodic table, the effective nuclear charge generally increases due to the addition of protons in the nucleus without a corresponding increase in shielding from inner electrons. This trend leads to a decrease in atomic radius and an increase in ionization energy, making it essential for predicting chemical behavior and reactivity.
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Periodic Trends
Related Practice
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. (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?

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?

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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Textbook Question
Which will experience the greater effect nuclear charge,the electrons in the n = 2 shell in F or the n = 2 shell in B?Which will be closer to the nucleus?
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Textbook Question
Arrange the following atoms in order of increasing effectivenuclear charge experienced by the electrons in the n = 2shell: Be, Br, Na, P, Se.