Sheets Page 1 Lecture 3 Lecture 3: Electronic structure of an atom Read: BLB 2.1, 2.2; 6.1–6.3 HW: BLB 6:4,10,13,23,26 Sup 6:1,3,4,5—do NOT do Sup 6.2! Know: • E = hν • c = λν • photons: quantized energy • photoelectric effect • line spectra • Bohr model • electronic transitions 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 Bonus deadline for Skill Check Tests 3 & 4 is Jan 29 Drop/add ends Wednesday, Jan 21Sheets Page 2 Lecture 3 Examples: a. What is the frequency of light if λ = 450 nm? b. What is the energy of one photon of 450 nm light? NOTE: E = hν is only for the energy of 1 photon! c. What is the energy of 1 mole of photons of 450 nm light? (Youʼll see these concepts again when we hit BLB Chap 18 & throughout the semester!) h = 6.63 ! 10"34J sE = h#c =!""=c!Sheets Page 3 Lecture 3 Photoelectric effect • direct observation of quantum effects (Einstein 1921 Nobel Prize) • electrons are emitted by metal only if light has frequency (i.e., energy) greater than certain minimum value—regardless of light intensity! • when electrons are emitted, the number emitted is proportional to the light intensity Ek = hν – Eb Ek = kinetic energy of photoelectron; E=1/2 mv2 hν = photon energy Eb = binding energySheets Page 4 Lecture 3 Line spectra of atoms • spectroscopy: study of light interacting with matter • spectrum: distribution of frequency in emitted radiation spectrum type νʼs example • monochromatic 1 lasers • continuous all hot solids • discrete (or line) a few gaseous atomsSheets Page 5 Lecture 3 Atomic spectra (cont.) • observation of line spectra implies that atoms have (quantized) frequencies & energy levels • in other words, atoms can have only preset energy values; most energy values cannot occur; only certain energy changes are possible for electrons • frequencies (ν) reflect of atoms • atoms have characteristic frequencies!Sheets Page 6 Lecture 3 Bohr model of H atom 1. atom is similar to planetary system with e– orbiting central nucleus (p+) 2. usual laws of physics hold except that only certain specific radii (orbits) are allowed; n = 1, 2, 3, 4, … 3. energies of the allowed states are En= !RH1n2" # $ % & ' n = 1, 2, 3, 4, … ∞ • RH = Rydberg constant = 2.18 × 10–18 J • n = integer, principal quantum number • as the allowed radii increase in a quantal fashion by n2, E decreases by 1/n2 NOTE: En is always negative! E !Q1Q2dSheets Page 7 Lecture 3 Electronic transitions in hydrogen • ground state is most stable with the largest (lowest) negative energySheets Page 8 Lecture 3 Bohr model of H atom (cont.) 4. atoms absorb or emit light of specific frequency (ν) when e− changes its orbit (i.e., a photon!) ΔE = Efinal – Einitial = hν or h!= RH1ninitial2"1nfinal2# $ % & ' ( where ninitial and nfinal are integers of orbits • predicts the H-atom spectrum exactly! if nfinal > ninitial, then ΔE is + ⇒ a photon if nfinal < ninitial, then ΔE is – ⇒ a photonSheets Page 9 Lecture 3 Example: What is the energy of an electron in a hydrogen atom with the principle quantum number of 6? A. –6.06 × 10–20 J B. –3.63 × 10–19 J C. –6.06 × 10–2 J D. 3.63 × 10–19 J E. 6.06 × 10–20 JSheets Page 10 Lecture 3 Example: Which of the following electronic transitions of the hydrogen atom emits a photon of the shortest wavelength? A. n = 6 → n = 3 B. n = 1 → n = 2 C. n = 3 → n = 2 D. n = 2 → n = 1 E. n = 2 → n = 4Sheets Page 11 Lecture 3 Before next class: 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 Answers: p 2: a. 6.67 × 1014 s–1; b. 4.42 × 10–19 J; c. 266 kJ p 9: A p 10:
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