Quantum Mechanical Model of Electronic Structure Solutions

Chem Worksheet - Week #9 - Solutions Quantum Mechanical Model of Electronic Structure Key Questions 1. 2. 3. The wave functions, which describe orbitals, are cast in terms of three quantum numbers. Fill in the table below with the name and allowed values for each quantum number. Number Name Allowed values n principal 1, 2, 3, ... l azimuthal 0, ..., n – 1 ml magnetic -l, (-l + 1), ..., 0, ..., (l - 1), l The table below shows various combinations of the three quantum numbers. Indicate which combinations are allowed and which are disallowed. For those that are allowed, give the subshell notation (e.g., 2p). n l ml Allowed? Notation 3 2 –1 yes 3d 4 0 0 yes 4s 2 2 1 no 5 1 1 yes 5p 4 3 –2 yes 4f 4 –3 0 no Describe the characteristic shapes of s, p, and d orbitals that distinguish them from each other? All s orbitals are spheres. The p orbitals have opposite lobes along an axis (“dumbbell” shape”). Four of the five d orbitals are clover-leaf shaped, and one (dz2) has a dumbbell and doughnut shape. 4. Which quantum number identifies the shape of an orbital? l, the azimuthal 5. What happens to the size and number of nodes of a particular type of orbital (e.g., ns orbitals) as the principal quantum number increases. As n increases, each orbital type gets larger and acquires an additional spherical node for every integer increase of n. 6. On the axes below, sketch a 3dxy orbital on the left and a 3dx2–y2 orbital on the right. y y x x Note that the lobes of the cloverleaf shape lie between the axes for a 3dxy orbital and on the axes for a 3dx2–y2 orbital. 7. In light of the Pauli Exclusion Principle, indicate the electron capacities of the following subshells: 3s 2p 5f 3d 2 6 14 10 8. In a one-electron atom the energy depends solely on n (e.g., 3s = 3p = 3d). In multielectron atoms, the energy depends on both n and l. List the following orbitals in order of increasing energy (i.e., most stable first): 4f, 3s, 4p, 2p, 3d. 2p < 3s < 3d < 4p < 4f 9. Write the complete electronic configuration for each of the following atoms in their ground states. 1s22s22p2 6C 1s22s22p63s23p5 17Cl 1s22s22p63s23p64s23d3 23V 1s22s22p63s23p64s2 20Ca 1s22s22p63s23p64s23d104p65s24d105p5 53I 1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p1 81Tl 10. Write the complete electronic configurations of these two elements. 1s22s22p63s23p64s13d5 not 1s22s22p63s23p64s23d4 24Cr 2 2 6 2 6 1 10 2 2 6 2 6 2 9 29Cu 1s 2s 2p 3s 3p 4s 3d not 1s 2s 2p 3s 3p 4s 3d 11. Looking at a periodic table, write down the valence configuration for each of the following elements. (Practice this on your own so that you can do this without hesitation.) 4s24p3 3d84s2 6s1 4d105s2 5s2 33As 28Ni 55Cs 48Cd 38Sr 12. Consider gold, 79Au, whose valence configuration is irregular in the same way as 29Cu and 47Ag. a. Write the valence configuration of 79Au in shell order. 5d106s1 (The fully-fill d subshell favors this over the aufbau expected 5d96s2.) b. Write the complete electronic configuration of 79Au in shell order. 1s22s22p63s23p63d104s24p64d104f145s25p65d106s1 c. Write the valence configuration of Au+ by removing one electron from the highest energy occupied subshell in the configuration of neutral Au. 5d106s0, or just 5d10 (Note that the first electron removed is from the 6s subshell.) d. Write the valence configuration of Au3+ by removing two electrons from the highest energy occupied subshell in the configuration of Au+. 5d8 13. Write the condensed electronic configurations for the elements whose valence configurations you wrote in Key Question 11, above. [Ar]3d104s24p3 [Ar]3d84s2 [Xe]6s1 33As 28Ni 55Cs [Kr]4d105s2 [Kr]5s2 38Sr 48Cd 14. Write the condensed electronic configurations for the following ions. 2– 2+ [Ar]3d104s24p6 = [Kr] [Kr] 34Se 38Sr 2+ 10 2+ [Kr]4d [Ar]3d6 48Cd 26Fe 3+ 5 + [Ar]3d [Xe]4f145d106s2 81Tl 26Fe 15. Draw box-and-arrow diagrams for the valence configurations of Fe, Fe2+, and Fe3+. Fe ¼¿ ¼ ¼ 3d ¼ ¼ Fe2+ ¼¿ ¼ ¼ 3d ¼ ¼ ¼ 3d ¼ Fe3+ ¼ ¼ ¼¿ 4s 4s ¼ 4s