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

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Identify the electron configuration of the element in question. Determine the number of electrons in each shell and subshell.

Apply Slater's rules to calculate the shielding constant (\( \sigma \)) for each electron. Remember that electrons in the same group, inner shells, and different shells contribute differently to the shielding.

Calculate the effective nuclear charge (\( Z_{\text{eff}} \)) using the formula: \( Z_{\text{eff}} = Z - \sigma \), where \( Z \) is the atomic number and \( \sigma \) is the total shielding constant.

Consider the contributions of different electron groups: Electrons in the same shell, electrons in the \( n-1 \) shell, and electrons in shells \( n-2 \) or lower, each with their respective shielding values.

Sum up the contributions from all electrons to find the total shielding constant, and use it to determine the effective nuclear charge.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Slater's Rules

Slater's Rules are a set of guidelines used to estimate the shielding effect of electrons in multi-electron atoms. They provide a systematic way to calculate the effective nuclear charge (Z_eff) experienced by an electron, taking into account the contributions of other electrons. By applying these rules, one can determine how much an electron is shielded from the full positive charge of the nucleus, which is crucial for understanding atomic structure and electron configurations.

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 is calculated by subtracting the shielding effect of other electrons from the actual nuclear charge. Z_eff influences various atomic properties, including ionization energy and atomic size, as it determines how strongly an electron is held by the nucleus. Understanding Z_eff is essential for predicting the behavior of atoms in chemical reactions.

Shielding Effect

The shielding effect refers to the phenomenon where inner-shell electrons partially block the attractive force of the nucleus on outer-shell electrons. This results in outer electrons experiencing a reduced effective nuclear charge. The extent of shielding varies depending on the electron configuration and the arrangement of electrons in an atom. Recognizing the shielding effect is vital for accurately calculating Z_eff and understanding trends in the periodic table.

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Textbook Question

Figure 7.4 shows the radial probability distribution functions for the 2s orbitals and 2p orbitals. (a) Which orbital, 2s or 2p, has more electron density close to the nucleus?

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?

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

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

Textbook Question

In Table 7.8, the bonding atomic radius of neon is listed as 0.58 Å, whereas that for xenon is listed as 1.40 Å. A classmate of yours states that the value for Xe is more realistic than the one for Ne. Is she correct? If so, what is the basis for her statement?

Textbook Question

The As ¬ As bond length in elemental arsenic is 2.48 Å. The Cl ¬ Cl bond length in Cl2 is 1.99 Å. (a) Based on these data, what is the predicted As ¬ Cl bond length in arsenic trichlo- ride, AsCl₃, in which each of the three Cl atoms is bonded to the As atom?