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exam quwtion exchange Periodic Chart Pedagogy Claude H. Yoder Franklin and Marshall College Lancaster. PA 17604
Carolyn S. Yoder Millersville University Millersville, PA 17551
The hierarchical relationship of the structure of the periodic chart, electron configuration, and the interrelationships of the quantum numbers is one of the most elegant and important discoveries of modern chemistry. We have found that a very effective pedagogical device for teaching this relationship is the use of a hypothetical set of quantum numbers, followed by the development of electron configurations and a periodic chart based on this set of quantum numhers. We offer helow two examples of questions based on hypothetical sets of relationships between the quantum numbers. In answering these questions we assume that the Pauli principle, Hund's first rule, the nomenclature for designating orhitals, and the usual relative energies of the orbitals for multielectron atoms apply.
JOHN
J.
ALEXANDER
University of Cincinnati Cincinnati. Ohio 45221
g. What is the atomic number of the first inert gas? h. Are these elements likely t o form +3 ions. Questions about the meaning of a magnetic quantum number of 1and the actual origins of the relationships between the quantum numbers would be more difficult, hut certainly instructive. 2. For the following hypothetical set of quantum numbers:
a. At what atomic number will the first f-filler appear? b. Would you predict that the 3s orbital would he lower in energy than the 2d? If not, what would the consequences he for the structure of the periodic chart?
Ouestlons 1. For the hypothetical set of quantum numbers:
a. How many s orhitals will there be in a given quantum level? h. How many p orbitals will there be in the third principle (n = 3) quantum level? c. Give the electron configuration of the element with atomic number 10. d. What is the atomic number of the first element in the d-fillers? e. How many transition elements are there in the first period that contains transition elements? f. Construct a periodic chart that obeys these rules for the quantum numhers.
Figure 1. Energy level diagram for questlon 1
Volume 67
Number 9
September 1990
759
s-fillers 1 1 2
1
p - f i1 l e r s
f-fillers Figure 3. Energy level diagram for question 2. Figure 2. Periodic chart fw questlon 1
Acceptable Answers 1. a. An s orbital has a n angular momentum quantum number, 1, of 0. The number of orbitals within a principal quantum level (for example n = 3) having a given angular momentum is determined by the number of possible values of the magnetic quantum number. In our hypothetical set of quantum numbers, m can have only one value and therefore there is only ones orbital, one p orbital, one d orbital, and so on within a oarticular auantum level. .~~ b. One. A porbiral occurs when 1 = 1, but m can haveonly onevalueso therecan beonlyone porbital inevery quantum I&& except the first. c. Fieure 1revresents the energy level diagram for the low lying atomic orbitals governed by this set of quantum numbers. Ten electrons will populate the first five energy levels (in the ground state) andthe electron configuration will be1s22s22p23s23pZ. d. Thirteen electrons are required to reach the 3d orbitals, and therefore the atomic number is 13. e. .. Because there is onlv one 3d orbital, there can only be two transition elements in this period. ~~
~~
f. Figure 2 shows the periodic chart derived from these quantum numbers. g. When the first quantum level (n = 1) is filled, we have the element with atomic number 2. h. Ions with a +3 charge are generally of doubtful existence (compounds containing these "ions" have a great deal of covalent character) but are even less likely with elements that obev these ouantum numbers. Elements of main group 111(atomic numliers 5,9,15,21, 29) can attain an in& gas configuration more easily by gaining one electron. Of course, the existence of ions of a particular charge depends on a varietv of factors-ionization energies or electron affinities, latticeenergies or heats of solutio< and so on. 2. a. The energy level diagram (Fig. 3) shows that f orbitals first appear for n = 3. Filling all the orbitals below the first 3f with two electrons (s = f112) requires 44 electrons. Hence, element 45 will be the first f-filler. b. If the spacing between energy levels is inversely proportional to n as in the real periodic chart, the spacing between the n = 2 and n = 3 levels is greater than that between n = 3 and n = 4. Thus. the 2d and 3s levels are less likely to display energy inversions than the 3d and 4s. Assumine this areument to be correct, the d-fillers will come a t and p-fillers rather than between them as in the en2 of the ithe real periodic chart.
Advances in New Materials: 15th Biennial Polymer Symposium The ACSDivision of Polymer Chemistry, Inc. will hold its 15th Biennial Polymer Symposiumon the topic, "Advances in New Materials", Novemher 17-21, 1990, Pier 66 Resort and Marina, Ft. Lauderdale, FL. A three-and-one-half-day program will be presented by recognized leaders in major areas of new polymeric materials. The topics will include advances in new high performance polymers, polymers for electronic applications, electrically conducting polymers, nonlinear optics, silicon- and zirconium-containing polymers, and polymers derived from biological media. The Polymer Division Award will be presented to M. Szwarc at an Award Banquet. The technical presentations will also be complemented by a poster session that will run during three morning sessions. Additional posters in the topic areas of this meeting are solicited. Further information regarding the program can he obtained from Dr. J. C. Salamone,7075Queenferry Circle, Boca Raton, FL 33496 (phone: (407)451-9260, FAX: (407)4519269.
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Journal of Chemical Education
