1Chem C1403 Lecture 9 Wednesday, October 5, 2005Today we’ll revisit the discharge lamp experimentswith an atomic and electronic interpretation based onthe Bohr atom.We’ll also review some of the key equations ofEinstein, Bohr and deBroglie that provide insight tothe paradigm shifts that lead to modern quantummechanics.We’ll then begin an examination of the modernquantum mechanical interpretation of the H atom.2Robert Grubbs: NobelPrize in Chemistry:2005New methods offorming polymers.Former graduate student at Columbia and formerfootball and basketball (he’s 6’ 5” tall) opponent!3James Clerk Maxwell1831-1879Key equations:c = λ ν λ (Gk lambda), ν(Gk nu)c = speed of light wave wave propagation λ = wavelength, ν = frequencyλLow FrequencyHigh FrequencyClassical Paradigm: Energy carried by a light wave isproportional to the Amplitude of wave. Big wave, small wave.Maxwell: Light consists of waves (energy is propagated bywaves): Energy is spread over space like an oscillating liquid.Maxwell’s theory is called the classical theory of light.λλλ4Waves and lightc = νλ = 3.0 x 108 m-s-1 = 3.0 x 1017 nm-s-1ν = c/λ, λ = c/νc = speed of lightν = frequency of lightλ = speed of lightA computation:What is the frequency of 500 nm light?Answer: ν = c/λ; ν = (3.0 x 1017 nm-s-1)/500 nm ν = 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 catastropheby quantizing the energy of light. Light canonly have energies given by E = hν.The valueof h = 6.6 x 10-34 Js fits experiment!Max PlanckNobel Prize 1918“for his explanation of theultraviolet catastrophe”, namelyE = hν, the energy of light isbundled and comes in quanta.if E = hνif 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 thephotoelectric effect”, namely,E2 - E1 = hν, light isquantized as photons.E2 - E1 = hνRed lightis “inert”to kickingout electrons,no matterwhat theamplitude ofthe light!Blue lightkicks outElectronseven atvery lowamplitude!The slope of KEMax vs ν is h!!!!!10Key equation: KEMAX = h(ν - ν0)Slope = h!!!!Φ = hν0 (work function to removethe electron from metal)= KEMAX = hν - hν0(Excess kinetic energy ofthe electron)11Interpreting data: Which metal takes least energyto eject an electron?12The Rutherford atom.The predicted death spiral ofthe Rutherford atom.Bohr solved this paradox and the paradox of the linespectra of atoms with an assumption and some algebra13Wavelength (λ) 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 thison the front podium.Let’s do an experiment: Look at the discharge lamps through thediffraction glasses. They work just like a prism and break up light into itscomponents. Notice the dark spots between the “lines” of the differentcolors. The number and positions of the lines are the unique signature ofthe elements. A lab experiment. Note the number and color of the lines.See if you can identify the element.You’ll see something like thisthrough your diffraction glasses!Lamp leftLamp right15Unknown16Certain orbits have special values of angular momentumand do not radiate:mever = n(h/2π) n = 1, 2, 3,….infinity(This solves the death spiral problem)The energy and frequency of light emitted or absorbed isgiven by the difference between the two orbit energies,e.g., E(photon) = E2 - E1 (Energy difference) = hν(This solves the line spectrum paradox)Niels BohrNobel Prize 1922“the structure of atoms and theradiation emanating from them”The basis of all photochemistryand spectroscopy!E1E2E2E1Photon absorbedPhoton emitted+ hν- hνPhoton absorbedPhoton emitted17But there was more,much more that Bohrdid than qualitativelytake care of the tworemaining paradoxes.He then applies somequantitative thinkingto figure out what thesize of the H atomwas based on hishypothesis and then tocompute the energiesof the jumps betweenorbits!1819By solving the line spectrum paradox, the Bohr model allowed thecomputation of the energy of an electron in a one electron atom: En = -Ry(Z2/n2) Ry = 2.18 x 10-18 JThe results of hiscomputationscompared veryfavorably withexperimental datafor one electronatoms, but failedcompletely foratoms with morethan one electron!Something wasstill missing!20Two seemingly incompatible conceptions can each represent anaspect of the truth ... They may serve in turn to represent the factswithout ever entering into direct conflict. de Broglie, DialecticaLouis de Broglie 1892-1987Nobel Prize 1929“for his discovery of the wave nature of electrons”Light: E = hν (Planck)Mass: E = mc2 (Einstein)thenhν = h(c/λ) = mc2 (de Broglie)Light = MatterWhat was missing? The electron was being treated as a particle. Ifwaves can mimic particles, then perhaps particles can mimic waves.λ = h/mv21Traveling waves and standing wavesLight as a traveling wave.No beginning and no endA circular standing waveWith 7 wavelengths around thecircle. Localized in space (on anatom!)λEvery wave has a corresponding“wavefunction” that completely describes allof its properties.22The wave properties of matter are only apparentfor very small masses of matter.λ = h/mvThe value ofh = 6.6 x 10-34 JsWavy cows?Electrons showwave 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: λ = h/mvh = 6.63 x 10-34 J-sm = 0.145 kg, v = 30 m-s-1λ = h/mv = 6.63 x 10-34 J-s/(0.145 kg, v = 30 m-s-1)λ = 1.5 x 10-34 m = 1.5 x 10-24 ÅThis is such a small number that it cannot be measured andcompletely masks the wave behavior of macroscopic objects.24Wave, particles and the Schroedinger equationDiffraction patterns:Constructive and destructiveinterference, the signaturecharacteristic of waves.Destructive interferenceConstructive interference25The electron as a boundwave: what is itswavefunction?λSchroedinger:wave equation andwavefunctions2627Wavefunctions and orbitalsAn orrbital is a wavefunctionObital: defined by the quantum numbers n, l and ml (which aresolutions of the wave equation)Orbital is a region of space occupied by an