10. Periodic Properties of the Elements

For a multielectron atom, a 3s orbital lies lower in energy than a 3p orbital because (LO 5.16) (a) a 3p orbital has more nodal surfaces than a 3s orbital. (b) an electron in a 3p orbital has a higher probability of being closer to the nucleus than an electron in a 3s orbital. (c) inner electrons shield electrons in a 3p orbital more effec-tively than electrons in a 3s orbital. (d) the energy of the electron can be spread between three 3p orbitals instead of only one 3s orbital.

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?

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

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.

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?

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?

Arrange the following atoms in order of increasing effective nuclear charge experienced by the electrons in the n = 2 shell: Be, Br, Na, P, Se.

Consider the isoelectronic ions F- and Na+. (b) Using Equation 7.1 and assuming that core electrons contribute 1.00 and valence electrons contribute 0.00 to the screening constant, S, calculate Zeff for the 2p electrons in both ions.

(a) From the data in Table 8.2, calculate the effective charges on the Br atom of the HBr molecule in units of the electronic charge, e.

(a) From the data in Table 8.2, calculate the effective charges on the H atom of the HBr molecule in units of the electronic charge, e.

Which experience a greater effective nuclear charge: the valence electrons in beryllium or the valence electrons in nitrogen? Why?

Arrange the atoms according to decreasing effective nuclear charge experienced by their valence electrons: S, Mg, Al, Si.

If core electrons completely shielded valence electrons from nuclear charge (i.e., if each core electron reduced nuclear charge by 1 unit) and if valence electrons did not shield one another from nuclear charge at all, what would be the effective nuclear charge experienced by the valence electrons of each atom? c. O

If core electrons completely shielded valence electrons from nuclear charge (i.e., if each core electron reduced nuclear charge by 1 unit) and if valence electrons did not shield one another from nuclear charge at all, what would be the effective nuclear charge experienced by the valence electrons of each atom? b. Ca

If core electrons completely shielded valence electrons from nuclear charge (i.e., if each core electron reduced nuclear charge by 1 unit) and if valence electrons did not shield one another from nuclear charge at all, what would be the effective nuclear charge experienced by the valence electrons of each atom? a. K

In Section 3.6, we estimated the effective nuclear charge on beryllium's valence electrons to be slightly greater than 2+. What would a similar treatment predict for the effective nuclear charge on boron's valence electrons? Would you expect the effective nuclear charge to be different for boron's 2s electrons compared to its 2p electron? In what way? (Hint: Consider the shape of the 2p orbital compared to that of the 2s orbital.)

Why is energy usually released when an electron is added to a neutral atom but absorbed when an electron is removed from a neutral atom?

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?

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

(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?

How does electron shielding in multielectron atoms give rise to energy differences among 3s, 3p, and 3d orbitals?

Order the electrons in the following orbitals according to their shielding ability: 4s, 4d, 4f.

One method for calculating Zeff is to use the equation

where E is the energy necessary to remove an electron from an atom and n is the principal quantum number of the elec-tron. Use this equation to calculate Zeff values for the highest-energy electrons in potassium (E = 418.8 kJ/mol) and krypton (E = 1350.7 kJ/mol).

Classify each statement about effective nuclear charge, 𝑍eff , as true or false.

Rank the elements by effective nuclear charge, 𝑍eff, for a valence electron.

In which orbital below would an electron (on average) be closest to the nucleus?