Fig. 2.9 of the notes contains a schematic drawing of the energy bands in sodium
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Question
Fig. 2.9 of the notes contains a schematic drawing of the energy bands in sodium (valence 1) as a function of the internuclear separation. Assume that a roughly similar diagram pertains to Mg (valence 2) and A1 (valence 3), which are the next two elements in the same row of the periodic table. [This is only true in a rough approximation. Mg and A1 do not even have the same crystal structure as Na. However, the three elements do have the common property that the bands arising from the 3s and 3p states overlap at separations near the equilibrium separation, r0.] Fig. 2.1: Energy bands as a function of internuclear distance in Na. Now suppose that you are given a means for controlling the internuclear separation precisely; for example, you may employ a well-disciplined troop of 1023 Maxwell demons who push the atoms apart or pull them together on command. Show that at a critical value of the equilibrium separation Mg changes from a metal to a semiconductor or insulator, but Na and A1 remain metallic until the atoms are pushed so far apart that they behave as independent atoms.Explanation / Answer
The number of electrons in an atom of an element corresponds to the element's Atomic Number (Z) and is equal to the number of protons in the nucleus of the atom. H atom, Z = 1. Number of protons in H atom = Z = 1 Number of electrons in H atom = Z = 1 The number of electrons in the ion of an element corresponds to the element's Atomic Number (Z) minus the charge on the ion: H+, Z = 1, charge = +1. Number of electrons in ion = Z - charge = 1 - (+1) = 0 H-, Z = 1 charge = -1. Number of electrons in ion = Z - charge = 1 - (-1) = 2 Simple Electron Configuration shows the number of electrons in each energy level Lowest Energy levels are filled first (ie, first energy level is filled first followed by the second then the third etc) Energy Level Maximum Number of Electrons First 2 Second 8 Third 18 Fourth 32 Filled energy levels correspond to the electron configuration of Group 18 (VIII) elements (the Noble or Inert Gases) Subshell Electron Configuration shows the number of electrons in each subshell (or sub-level) within each energy level Group of the Periodic Table subshell being filled Maximum Number of Electrons 1 and 2 (IA and IIA) s 2 13, 14 , 15 , 16 , 17 , 18 (IIIA,IVA,VA,VIA,VIIA,VIII) p 6 Transition Metals d 10 Lanthanides and Actinides f 14 Orbital Notation shows the number of electrons in each orbital within an energy level Simple Electron Configuration Maximum number of electrons in each energy level (shell): 1st(K)=2, 2nd(L)=8, 3rd(M)=18, 4th(N)=32 The helium atom has 2 electrons in the first energy level. Its simple electron configuration is 2 The neon atom has 10 electrons, 2 electrons in the first energy level and 8 electrons in the second energy level. Its simple electron configuration is 2,8 The argon atom has 18 electrons, 2 electrons in the first energy level, 8 electrons in the second energy level, 8 electrons in the thrid energy level. Its simple electron configuration is 2,8,8
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