Sheets Page 1 Lecture 4 Lecture 4: Electronic structure of an atom Read: BLB 6.3–6.6 HW: BLB 6:33,39,51,54 Sup 6:6,7,8,10—no Sup 6.9!!! Know: • matter waves • uncertainty principle • electronic transitions of orbitals • quantum numbers (n, , m, ms) • orbitals: their shapes and energies Drop/add ends TODAY, Wednesday, Jan 21 Bonus deadline for Skill Check Tests 3 & 4 is Jan 29 (Thursday) Exam 1: Monday, Feb 9 @ 6:30!!! Form a study group, use the CRC, take advantage of SI (info on web), use the online resources, and work those problems—practice, practice, practice Sheets’s office hours: Mondays 12:30-2; Tuesdays 10:30-12 in 324 Chem (or 326 Chem).Sheets Page 2 Lecture 4 Dual nature of electrons • Bohr model: explained some experimental evidence for H atom, but it failed for other atoms—why was this?? • DeBroglie: if light has a dual wave/particle nature, then why doesnʼt matter have a dual wave/particle nature—hmmm… λ = h/mv m = mass v = velocity h = Planckʼs constant NOTE: mv = momentum (particle nature) and λ referred to as a “matter wave” (wave nature) • effects observable only for extremely small mass: for a baseball or bacteria, λ is too small to observe; but for e–, λ is of atomic size producing profound effects • electron waves discovered in 1927 (Davidson & Garmer); basis for electron microscope (electrons diffract when interacting with matter)Sheets Page 3 Lecture 4 Heisenberg uncertainty principle • derives from wavelike nature of matter • it is NOT possible to simultaneously know the position & velocity (momentum, mv) of a particle with complete certainty • this really becomes important when dealing with subatomic matter • all electrons have a velocity, therefore, you cannot specify their exact location • itʼs not appropriate to imagine e– moving in nice little orbits around the nucleus • contradicts Bohrʼs planetary model of H atom • so, can we say anything about where the e– are?!?Sheets Page 4 Lecture 4 The Schrödinger wave equation • takes into account both particle & wave terms HΨ = EΨ • Ψ(x,y,z) = wave function (shape) but • Ψ2(x,y,z) = probability of finding one e– in a region of space that is referred to as or probability density • electrons in atoms behave as “standing” waves! • think of e– as clouds of e– densitySheets Page 5 Lecture 4 The Schrödinger wave equation (cont.) • orbitals: Ψ2(x,y,z) [modern view of atomic structure] specify probability of finding an e– in a given region of space (i.e., have ) specify of that e– are characterized by 3 different quantum numbersSheets Page 6 Lecture 4 Figure from Moore, Stanitski, Jurs (2005) Chemistry: The Molecular Science; Thomson Brooks/ColeSheets Page 7 Lecture 4 Quantum numbers 1. principal quantum number (n): determines info about the shell & ; modern equivalent to n in Bohr model n = (+ intergers) 2. azimuthal quantum number ( ): determines info about orbital = NOTE: use symbols rather than numbers for = 0 1 2 3 name= 3. magnetic quantum number (m): determines orbitalʼs 3D ; a range of numbers m = (including 0)Sheets Page 8 Lecture 4 Review of orbitals • orbitals: region of space with size, shape and characteristic energy orbital name # of orbitals shape s ( = 0) sphere radially symmetric p ( = 1) dumbbell (2 lobes & node in center) d ( = 2) clover & 1 2-lobes & collar different from p-orbitals!!! f ( = 3) yikes!!?!!?! • node @ Ψ2 = 0 note: E ↑ as # nodes ↑ • check out http://www.weizmann .ac.il/home/comartin/orbitals.html; the “Grand Orbital Table” is nifty!Sheets Page 9 Lecture 4 Even more about orbitals • shell: defined by quantum number n • subshell: defined by quantum numbers n, e.g., 3s (n = 3, = 0) 2p (n = 2, = 1) • when orbitals of the same subshell have the same energy: they are degenerate • orbital: defined by quantum numbers n,, m e.g., 2px (n = 2, = 1) 2py (n = 2, = 1) 2pz (n = 2, = 1) and m = –1, 0, 1 when = 1 NOTE: all of these have the same energySheets Page 10 Lecture 4 More about orbitals e.g., 3d n= 3 = m = orbitals in subshell • recall, higher energy ⇒ more nodes (e.g., BLB Fig. 6.18); node @ Ψ2 = 0 note: E ↑ as # nodes ↑ • n2 = total number of orbitals in the nth shell • see BLB Table 6.2; you now know enough to make up this table!Sheets Page 11 Lecture 4 Before next class: Read: BLB 6.7–6.9 HW: BLB 6:59,63,67,71,74,75,90,97 Sup 6:11–15 Know: • orbitals & atoms with >1 electrons • Pauli exclusion principle • Hundʼs rule • electronic configurations of
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