Slide 1Slide 2Upcoming schedule—compare to syllabusde Broglie’s Novel NotionSlide 5Werner HeisenbergHeisenberg’s Uncertainty PrincipleErwin SchrodingerElectron CharacteristicsBaseball v. ElectronWhat if a baseball behaved like an electron?Slide 12Bohr Model v. Quantum MechanicsQuantum Mechanics ModelQuantum Mechanics Model Describes the energy, arrangement and space occupied by electrons in atoms“Most Successful Theory of the 20th Century”Quantum Mechanics Model Describes the energy, arrangement & space occupied by electronsConcept CheckReminder about SI UnitsSlide 20Slide 21Implication of Heisenberg’s Uncertainty PrincipleDartboard AnalogyResults from Schrodinger’s Wave EquationSlide 25Slide 26Slide 27Slide 28Representing s OrbitalsSlide 30Slide 31Slide 32Principal Quantum Number & Energy SublevelsSlide 34Slide 35Slide 36Why are atoms spherical?Quantum numbers and orbital energies Each electron in an atom has a unique set of quantum numbers to define it { n, l, ml, ms }Quantum numbers and orbital energies Each atom’s electron has a unique set of quantum numbers to define it { n, l, ml, ms }Concept: Each electron in an atom has a unique set of quantum numbers to define it { n, l, ml, ms }Slide 41Average = 77.3Average = 156A= 188+A- = 181-187B+ = 175-180B= 165-174B- = 155-164C+ = 150-154C= 140-149C- =130-139Upcoming schedule—compare to syllabus•Homework 3 due Monday•Homework 4 due as usual•Homework 5—no credit—it’s open now for review.•Lecture: We’ll have lecture all week. Exam 3 will be over the weekend—format tba…..de Broglie’s Novel NotionLight was “known” (thought) to be a wave, but Light was “known” (thought) to be a wave, but Einstein showed that it also acts particle-like.Einstein showed that it also acts particle-like.Electrons were “known” to be particles mass & charge.Electrons were “known” to be particles mass & charge.French physicist:French physicist: What if ……What if ……1923electrons behaved as waves also Diffraction pattern obtained by firing a beam of electrons through a crystal.Dr. Quantum videoDr. Quantum videoWerner Heisenberg•In 1927, German physicist, proposed that the In 1927, German physicist, proposed that the dual nature of dual nature of the electronthe electron places limitations on how precisely we can know places limitations on how precisely we can know both the location and speed of the electronboth the location and speed of the electron•Instead, we can only describe electron behavior in terms of Instead, we can only describe electron behavior in terms of probabilityprobabilityThe Uncertainty PrinciplespeedspeedpositionpositionHeisenberg’sUncertainty PrincipleWave behavior limits what can be known!Wave behavior limits what can be known!•What if the particle has a small mass?What if the particle has a small mass?•What if the electron’s position is known very precisely?What if the electron’s position is known very precisely?•What if the electron’s speed is known very precisely?What if the electron’s speed is known very precisely? (±x)(±v(±x)(±vxx)) Can the electron’s orbit be precisely defined?± position ± speed hh44mmErwin Schrodinger•In 1926, Austrian physicist, proposed an equation that In 1926, Austrian physicist, proposed an equation that incorporates both the wave and particle behavior of the incorporates both the wave and particle behavior of the electronelectron•When applied to hydrogen’s 1 electron atom, solutions provide When applied to hydrogen’s 1 electron atom, solutions provide the the most probable locationmost probable location of finding the electron in the first of finding the electron in the first energy levelenergy level•Can be applied to more complex atoms too!Can be applied to more complex atoms too!Wave Equation & Wave Mechanics•Extremely small mass•Located outside the nucleus•Moving at very high speeds•Have specific energy levels•Standing wave behavior•Extremely small mass•Located outside the nucleus•Moving at very high speeds•Have specific energy levels•Standing wave behaviorElectron CharacteristicsA baseball behaves as a particle and follows a predictable path.BUT An electron behaves as a wave, and its path cannot be predicted. All we can do is to calculate the probability of the electron following a specific path. Baseball v. ElectronWhat if a baseball behaved like an electron?Characteristic wavelength ()• baseball 10-34 m• electron 0.1 nmSo, all we can predict is….. == hh /(/(mumu))massspeed“deterministic”“probabilistic”Bohr Model v. Quantum MechanicsEnergyElectronPosition/PathElementsBohr Quantum MechanicsThe electron's movement cannot be known precisely. We can only map the probability of finding the electron at various locations outside the nucleus. The probability map is called an orbital.The orbital is calculated to confine 99% of electron’s range.Energy of the electron is quantized into sublevels.Quantum Mechanics ModelQuantum Mechanics ModelDescribes the energy, arrangement and space occupied by electrons in atomsQuantumMechanicsElectron’s energy is quantizedMathematics of waves to define orbitals(wave mechanics)“Most Successful Theory of the 20th Century”DaltonThomsonRutherfordNewtonMaxwellPlankEinsteinMatterLight SchrödingerHeisenbergWaveMechanicsQuantumMechanicsBohr &de Broglie17Quantum Mechanics ModelDescribes the energy, arrangement & space occupied by electronsQuantumMechanicsElectron’s energy is quantizedMathematics of waves to define orbitals(wave mechanics)18Concept CheckIn Nature, which of the following are quantized? A) massB) chargeC) energy19Reminder about SI Units•mass [=] kg length [=] m time [=] s•Planck’s constant •Speed of light EE == hh inin HzHz ( (ss-1-1))hh == 6.6266.626 xx 1010-34-34 J·s J·scc == inin mm && inin HzHzcc == 2.9982.998 xx 101088 m/s m/s20Concept Check ==hh /(/(mumu))massspeedAn particle has a mass of 4.0 amu. If it travels at 0.20 as fast as the speed of light, what is its de Broglie wavelength? (1 amu = 1.66 x 10-27 kg)cc = 2.998 = 2.998 xx 101088 m/s m/shh = 6.626 = 6.626 xx 1010-34-34 J·sJ·s21Concept CheckA single pulse of a nitrogen gas laser, with a wavelength of 337 nm, contains 3.83 mJ of energy. How many photons does the pulse emit?hh = 6.626 = 6.626
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