1. How many orbitals are there in a shell of principal quantum number n? (Hint: begin with n = 1, 2, and 3 and see if you can recognize the pattern.)
2. a) On a single graph, sketch the radial wavefunctions for the 4f and 5f orbitals. b) On a single graph, sketch the radial probability functions for the 4f and 5f orbitals. c) Sketch all of the angular wavefunctions for the 4d orbitals.
3. Give the ground-state electron configurations and ground state term symbol of (a) Sc, (b) V3+, (c) Mn2+, (d) Cr2+, (e) Co3+, (f) Cr6+, (g) Cu, (h) Gd3+.
4. Give the ground-state electron configuration and ground state term symbol of (a) W, (b) Rh3+, (c) Eu3+, (d) Eu2+, (e) V5+, (f) Mo4+.
5. Give the ground-state electron configuration and ground state term symbol of (a) C, (b) F, (c) Ca, (d) Ga3+, (e) Bi, (f) Pb2+.
6. Find the electron configuration and ground state term symbol for the following species: Cl, Cl–, Mo, Mo+, Mo2+, Mo3+.
7. Write the electron configuration and give the ground state term symbol for: a) Fe; b) Fe2+; c) Ir+; d) Ir3+; and e) I–.
8. Write the electron configuration and give the ground state term symbol for: a) Ni; b) Ni2+; c) Rh+; d) Rh3+; and e) S2–.
9. Compare the first ionization energy of calcium with that of zinc. Explain the difference in terms of the balance between shielding with increasing numbers of d electrons and the effect of increasing nuclear charge.
10. Compare the first ionization energies of strontium, barium, and radium. Relate the irregularity to the lanthanide contraction.
11. The second ionization energy of some Period 4 elements are
ElementIE (kJ/mol)
Ca1145
Sc1235
Ti1310
V1365
Cr1592
Mn1506
Identify the orbital from which ionization occurs and account for the trend in the values.
12. The ionization energies of rubidium and silver are respectively 4.18 eV and 7.57 eV. Calculate the ionization energies of an H atom with its electron in the same orbitals as in these two atoms and account for the differences in values.
13. In general, ionization energies increase across a period from left to right. Explain why the second ionization energy of chromium is higher, not lower, than that of manganese.
14. It has been proposed that the ionization energy is proportional to Z*2/n2, where Z* is the effective nuclear charge and n is the principal quantum number. Make a plot of IE (x-axis) vs. Z*2/n2 (y-axis). Is the assertion justified? Why or why not? Are there exceptions to the generalization? If so, what are those exceptions and can you rationalize them?
15. Make a plot of IE vs. χ (χ = Pauling electronegativity) for the elements 1 through 18. Does your graph suggest any relationship between the two quantities? Why or why not?
16. Account for the fact the two Group 5 elements niobium (Period 5) and tantalum (Periodic 6) have the same metallic radii.
17. Consider the process of shielding in atoms, using Be as an example. What is being shielded? What is it being shielded from? What is doing the shielding?
18. Compare the broad trends in ionization energy, atomic radius, and electronegativity. Account for the parallels.