Lecture 4: Electronic structure of an atom
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1 Lecture 4: Electronic structure of an atom Read: BLB 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, m s ) 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 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 1 Lecture 4
2 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 2 Lecture 4
3 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 3 Lecture 4
4 The Schrödinger wave equation takes into account both particle & wave terms HΨ = EΨ Ψ(x,y,z) = wave function (shape) but Ψ 2 (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 density Sheets Page 4 Lecture 4
5 The Schrödinger wave equation (cont.) orbitals: Ψ 2 (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 numbers Sheets Page 5 Lecture 4
6 Figure from Moore, Stanitski, Jurs (2005) Chemistry: The Molecular Science; Thomson Brooks/Cole Sheets Page 6 Lecture 4
7 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 name= = magnetic quantum number (m ): determines orbitalʼs 3D ; a range of numbers m = (including 0) Sheets Page 7 Lecture 4
8 Review of orbitals orbitals: region of space with size, shape and characteristic energy orbital name # of orbitals shape s ( = 0) p ( = 1) d ( = 2) f ( = 3) sphere radially symmetric dumbbell (2 lobes & node in center) clover & 1 2-lobes & collar different from p-orbitals!!! yikes!!?!!?! Ψ 2 = 0 note: E as # nodes check out the Grand Orbital Table is nifty! Sheets Page 8 Lecture 4
9 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., 2p x (n = 2, = 1) 2p y (n = 2, = 1) 2p z (n = 2, = 1) and m = 1, 0, 1 when = 1 NOTE: all of these have the same energy Sheets Page 9 Lecture 4
10 More about orbitals e.g., 3d n= 3 = m = orbitals in subshell recall, higher energy more nodes (e.g., BLB Fig. 6.18); Ψ 2 = 0 note: E as # nodes n 2 = total number of orbitals in the n th shell see BLB Table 6.2; you now know enough to make up this table! Sheets Page 10 Lecture 4
11 Before next class: Read: BLB 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 atoms Sheets Page 11 Lecture 4
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