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

Problem 81c

Chapter 7, Problem 81c

(c) Detailed calculations indicate that the effective nuclear charge is 5.6+ for the 3s electrons and 4.9+ for the 3p electrons. Why are the values for the 3s and 3p electrons different?

Verified step by step guidance

Understand the concept of effective nuclear charge (Z_eff), which is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the shielding effect caused by other electrons.

Recognize that electrons in different orbitals experience different levels of shielding. The 3s and 3p orbitals have different shapes and distances from the nucleus, affecting their shielding and Z_eff.

Note that 3s electrons are closer to the nucleus and penetrate the inner electron shells more effectively than 3p electrons. This means 3s electrons experience less shielding and a higher Z_eff.

Understand that 3p electrons are further from the nucleus and are more shielded by inner electrons compared to 3s electrons, resulting in a lower Z_eff.

Conclude that the difference in Z_eff values for 3s and 3p electrons is due to their different orbital shapes and penetration levels, affecting the extent of shielding they experience.

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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 (the number of protons) minus the shielding effect of other electrons. This concept is crucial for understanding how electrons are held in an atom and why different types of electrons (like 3s and 3p) experience different levels of attraction to the nucleus.

Electron Shielding

Electron shielding occurs when inner-shell electrons repel outer-shell electrons, reducing the effective nuclear charge felt by those outer electrons. This phenomenon explains why electrons in different subshells (like 3s and 3p) can experience different effective nuclear charges, as the spatial distribution and energy levels of these electrons influence how much they are shielded from the nucleus.

Subshell Energy Levels

Subshell energy levels refer to the different energy states of electrons within an atom, categorized into s, p, d, and f orbitals. The 3s and 3p subshells have different shapes and orientations, leading to variations in their energy and the extent to which they are shielded by other electrons. This difference in energy levels contributes to the distinct effective nuclear charges experienced by 3s and 3p electrons.

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Related Practice

Textbook Question

(d) If you remove a single electron from a P atom, which orbital will it come from?

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Textbook Question

(b) Repeat these calculations using Slater’s rules.

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Textbook Question

In Table 7.8, the bonding atomic radius of neon is listed as58 pm, whereas that for xenon is listed as 140 pm. A classmateof yours states that the value for Xe is more realisticthan the one for Ne. Is she correct? If so, what is the basisfor her statement?

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Textbook Question

(a) If the core electrons were totally effective at screening the valence electrons and the valence electrons provided no screening for each other, what would be the effective nuclear charge acting on the 3s and 3p valence electrons in P?

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Textbook Question

Figure 7.4 shows the radial probability distribution functions for the 2s orbitals and 2p orbitals. (b) How would you modify Slater's rules to adjust for the difference in electronic penetration of the nucleus for the 2s and 2p orbitals?

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