The periodic system of the elements in our three-dimensional world is based on the four electron quantum numbers n = 1, 2, 3,....; l = 0, 1,....,n – 1, m = 0, ± 1, ± 2,...., ± 1; and s = ± 1/2. In Flatlandia, a two-dimensional world, the periodic system is thus based on three electron quantum numbers: n = 1,2,3,...; ml = 0, ±1, ±2, ...., ± (n-1); and s = ±1/2 where ml plays the combined role of l and ml of the three dimensional world. The following tasks relate to this two-dimensional world, where the chemical and physical experience obtained from our world is supposed to be still applicable.
(a) Draw the first four periods of the Flatlandian periodic table of the elements. Number them according to their nuclear charge. Use the atomic numbers (Z) as symbols of the specific element. Write the electron configuration for each element.
(b) Draw the hybrid orbitals of the elements with n = 2. Which element is the basis for the organic chemistry in Flatlandia? Find the Flatlandian analogous for ethane, ethene and cyclohexane. What kind of aromatic ring compounds are possible?
(c) Which rules in Flatlandia correspond to the octet and the 18-electron rules in the three dimensional world?
(d) Predict graphically the trends in the first ionization energies of the Flatlandian elements with n = 2. Show graphically how the electronegativities of the elements increase in the Flatlandian periodic table.
(e) Draw the molecular orbital energy diagrams of the neutral homonuclear diatomic molecules of the elements with n = 2. Which of these molecules are stable in Flatlandia?
(f) Consider simple binary compounds of the elements (n = 2) with Z = 1. Draw their Lewis structure, predict their geometries and propose analogues for them in the three dimensional world.
(g) Consider elements with n ≤ 3. Propose an analogue and write the chemical symbol from our world for each of these Flatlandian elements. On the basis of this chemical and physical analogue predict which two-dimensional elements are solid, liquid or gaseous at normal pressure and temperature.
