Ch.7 - Periodic Properties of the Elements

Problem 17

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Chapter 7, Problem 17

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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Identify the concept of effective nuclear charge (Z_eff), which is the net positive charge experienced by an electron in a multi-electron atom.

Recall that Z_eff is calculated using the formula: Z_eff = Z - S, where Z is the atomic number and S is the shielding constant.

Compare the atomic numbers of Argon (Ar) and Krypton (Kr). Ar has an atomic number of 18, while Kr has an atomic number of 36.

Consider the shielding effect: Electrons in inner shells shield outer electrons from the full charge of the nucleus. Since Kr has more inner electrons than Ar, the shielding effect is greater in Kr.

Determine which electrons are closer to the nucleus: Electrons experiencing a higher Z_eff are more strongly attracted to the nucleus and are likely to be closer. Compare the Z_eff for the n=3 shell electrons in Ar and Kr to determine which is closer.

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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 refers to the net positive charge experienced by an electron in an atom. It accounts for the actual nuclear charge (the number of protons) and the shielding effect caused by other electrons. As more electrons are added to an atom, the inner electrons shield the outer electrons from the full charge of the nucleus, affecting their energy levels and proximity to the nucleus.

Electron Shells and Energy Levels

Electron shells are defined energy levels where electrons reside around the nucleus of an atom. The principal quantum number (n) indicates the shell's energy level, with higher values corresponding to greater distances from the nucleus. In this context, both Argon (Ar) and Krypton (Kr) have electrons in the n=3 shell, but the number of protons in the nucleus influences the effective nuclear charge experienced by these electrons.

Atomic Size and Nuclear Attraction

Atomic size is influenced by the balance between the attractive forces of the nucleus and the repulsive forces between electrons. As the effective nuclear charge increases, electrons are pulled closer to the nucleus, resulting in a smaller atomic radius. In comparing Ar and Kr, the greater number of protons in Kr leads to a higher effective nuclear charge, making its n=3 electrons more likely to be closer to the nucleus than those in Ar.

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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 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

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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Textbook Question

With the exception of helium, the noble gases condense to form solids when they are cooled sufficiently. At temperatures below 83 K, argon forms a close-packed solid whose structure is shown below. (b) Is this value larger or smaller than the bonding atomic radius estimated for argon in Figure 7.7?

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Textbook Question

With the exception of helium, the noble gases condense to form solids when they are cooled sufficiently. At temperatures below 83 K, argon forms a close-packed solid whose structure is shown below. (c) Based on this comparison would you say that the atoms are held together by chemical bonds in solid argon?

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