PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 421Chem C1403 Lecture 9 Wednesday, October 5, 2005Today we’ll revisit the discharge lamp experiments with an atomic and electronic interpretation based on the Bohr atom.We’ll also review some of the key equations of Einstein, Bohr and deBroglie that provide insight to the paradigm shifts that lead to modern quantum mechanics. We’ll then begin an examination of the modern quantum mechanical interpretation of the H atom.2Robert Grubbs: Nobel Prize in Chemistry:2005New methods of forming polymers.Former graduate student at Columbia and former football and basketball (he’s 6’ 5” tall) opponent!3James Clerk Maxwell1831-1879Key equations:c =   (Gk lambda), (Gk nu) c = speed of light wave wave propagation = wavelength,  = frequencyLow FrequencyHigh FrequencyClassical Paradigm: Energy carried by a light wave is proportional to the Amplitude of wave. Big wave, small wave.Maxwell: Light consists of waves (energy is propagated by waves): Energy is spread over space like an oscillating liquid.Maxwell’s theory is called the classical theory of light. 4Waves and lightc = = 3.0 x 108 m-s-1 = 3.0 x 1017 nm-s-1= c/,  = c/ c = speed of light= frequency of light= speed of lightA computation:What is the frequency of 500 nm light?Answer: = c/= (3.0 x 1017 nm-s-1)/ = 6 x 1014 s-15Fig 16-564 paradoxes that doomed the classical paradigm of light (and matter)Ultraviolet catastrophePhotoelectric effectDeath spiral of the electronLine spectra of atom7Planck explains the ultraviolet catastrophe by quantizing the energy of light. Light can only have energies given by E = hThe value of h =6.6 x 10-34 Js fits experiment!Max PlanckNobel Prize 1918“for his explanation of the ultraviolet catastrophe”, namely E = h, the energy of light is bundled and comes in quanta.if E = hif E can be anything8Einstein’s explanation of the photoelectric effect” Light consists of photons which carry quanta of energy.9Albert EinsteinNobel Prize 1921“For his explanation of the photoelectric effect”, namely,E2 - E1 = h, light is quantized as photons. E2 - E1 = hRed light is “inert”to kickingout electrons, no matter what the amplitude of the light!Blue lightkicks outElectrons even at very low amplitude!The slope of KEMax vs  is h!!!!!10Key equation: KEMAX = h( - 0)Slope = h!!!! (work function to remove the electron from metal)= KEMAX = h - h0(Excess kinetic energy of the electron)11Interpreting data: Which metal takes least energy to eject an electron?12The Rutherford atom.The predicted death spiral of the Rutherford atom.Bohr solved this paradox and the paradox of the line spectra of atoms with an assumption and some algebra13Wavelength () Color656.2 red486.1 blue-green434.0 blue-violet410.1 violethttp://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/bohr.html14You’ll see something like this on the front podium.Let’s do an experiment: Look at the discharge lamps through the diffraction glasses. They work just like a prism and break up light into its components. Notice the dark spots between the “lines” of the different colors. The number and positions of the lines are the unique signature of the elements. A lab experiment. Note the number and color of the lines. See if you can identify the element.You’ll see something like this through your diffraction glasses!Lamp leftLamp right15Unknown16Certain orbits have special values of angular momentum and do not radiate:mever = n(h/2) n = 1, 2, 3,….infinity(This solves the death spiral problem)The energy and frequency of light emitted or absorbed is given by the difference between the two orbit energies, e.g., E(photon) = E2 - E1 (Energy difference) = h(This solves the line spectrum paradox)Niels BohrNobel Prize 1922“the structure of atoms and the radiation emanating from them”The basis of all photochemistryand spectroscopy!E1E2E2E1Photon absorbedPhoton emitted+ hν- hνPhoton absorbedPhoton emitted17But there was more, much more that Bohr did than qualitatively take care of the two remaining paradoxes. He then applies some quantitative thinking to figure out what the size of the H atom was based on his hypothesis and then to compute the energies of the jumps between orbits!1819By solving the line spectrum paradox, the Bohr model allowed the computation of the energy of an electron in a one electron atom: En = -Ry(Z2/n2) Ry = 2.18 x 10-18 JThe results of his computations compared very favorably with experimental data for one electron atoms, but failed completely for atoms with more than one electron!Something was still missing!20Two seemingly incompatible conceptions can each represent an aspect of the truth ... They may serve in turn to represent the facts without ever entering into direct conflict. de Broglie, Dialectica Louis de Broglie 1892-1987Nobel Prize 1929“for his discovery of the wave nature of electrons”Light: E = h (Planck)Mass: E = mc2 (Einstein)thenhh(c/)=mc2 (de Broglie)Light = MatterWhat was missing? The electron was being treated as a particle. If waves can mimic particles, then perhaps particles can mimic waves.  = h/mv21Traveling waves and standing wavesLight as a traveling wave. No beginning and no endA circular standing waveWith 7 wavelengths around the circle. Localized in space (on an atom!)Every wave has a corresponding “wavefunction” that completely describes all of its properties.22The wave properties of matter are only apparent for very small masses of matter.= h/mvThe value of h = 6.6 x 10-34 JsWavy cows?Electrons show wave properties, cows do not.23A computations of the wavelength of a macroscopic object (smaller than a cow): A baseball of 0.145 kg of mass, traveling at 30 m-s-1DeBrolie equation: = h/mvh = 6.63 x 10-34 J-sm = 0.145 kg, v = 30 m-s-1= h/mv = 6.63 x 10-34 J-s/(0.145 kg, v = 30 m-s-1)= 1.5 x 10-34 m = 1.5 x 10-24 ÅThis is such a small number that it cannot be