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Metal e-e- e-e- e-e- e-e- e-e- e+e+

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Faraday’s experiment (1833) Dissolve one mole of some substance in water Let an electric current run through it Measure how much charge runs through before it stops Na + Cl - +– All ions have the same charge (or simple multiples of that charge) Avogadro’s number was not known at this time

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J.J. Thomson discovers electron: 1897 e-e- Charged particle, bends in presence of magnetic field Relativity not discovered until 1905 Velocity measured with help of electric field +– Ratio of charge to mass now known

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The Plum Pudding Model: 1904 Electrons have only tiny fraction of an atom’s mass Atoms have no net charge 1904: J.J. Thomson proposes the “Plum Pudding” Model Electrons “imbedded” in the rest of the atom’s charge Rest of charge is spread throughout the atom

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Millikan measures charge e: 1909 Atomizer produced tiny drops of oil; gravity pulls them down Atomizer also induces small charges Electric field opposes gravity If electric field is right, drop stops falling +

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Millikan always found the charge was an integer multiple of e Millikan measures charge e: 1909 The atom in 1909: Strong evidence for atoms had been found Avogadro’s number, and hence the mass of atoms, was now known Electron mass and charge were known Atoms contained negatively charged electrons The electrons had only a tiny fraction of the mass of the atom Distribution and nature of the positive charge was unknown Meanwhile...

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Statistical Mechanics The application of statistics to the properties of systems containing a large number of objects Mid – late 1900’s, Statistical Mechanics successfully explains many of the properties of gases and other materials Kinetic theory of gases Thermodynamics The techniques of statistical mechanics: When there are many possibilities, energy will be distributed among all of them The probability of a single “item” being in a given “state” depends on temperature and energy gravity Gas molecules in a tall box:

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Announcements ASSIGNMENTS DayRead QuizHomework TodaySec. 3-2 Quiz HHwk. H FridayStudy For Testnone MondaySec. 3-3 & 3-4 Quiz IHwk. I Equations for Test: Force and Work Equations added Lorentz boost demoted 9/16 Test Friday: Pencil(s) Paper Calculator

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Black Body Radiation: Light in a box Consider a nearly enclosed container at uniform temperature: Light gets produced in hot interior Bounces around randomly inside before escaping Should be completely random by the time it comes out Pringheim measures spectrum, 1899 u( ) = energy/ volume /nm

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Black Body Radiation Can statistical mechanics predict the outcome? Find effects of all possible electromagnetic waves that can exist in a volume Two factors must be calculated: n( ): Number of “states” with wavelength E: Average energy Finding n( ) How many waves can you fit in a given volume? Leads to a factor of 1/ 4 What are all the directions light can go? Leads to a factor of 4 How many polarizations? Leads to a factor of 2 Goal - Predict:

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How to find E What does E mean? It is an expectation value Example: Suppose you roll a fair die. If you roll 1 you win $3, if you roll 2 or 3 you win $1, but if you roll 4, 5, or 6, you lose $2. What is the expectation value of the amount of money you win? Sum of all probabilities must be 1 What do we do with these sums over energy?

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What do we do with the sums? Energy can be anything Replace sums by integrals? Waves of varying strengths with the same wavelength The ultraviolet catastrophe

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Comparison Theory vs. Experiment: Theory Experiment What went wrong? Not truly in thermal equilibrium? Possible state counting done wrong? Sum Integral not really valid? Max Planck’s strategy (1900): Assume energy E must always be an integer multiple of frequency f times a constant h E = nhf, where n = 0, 1, 2, … Perform all calculations with h finite Take limit h 0 at the end

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Math Interlude: Take d/dx of this expression... Multiply by x... Some math notation:

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Planck’s computation: From waves:

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Planck’s Black Body Law Max Planck’s strategy (1900): Take limit h 0 at the end Except, it fit the curve with finite h! Planck Constant “When doing statistical mechanics, this is how you count states”

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Total Energy Density Let = hc/xk B T

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Wien’s Law For what wavelength is this maximum?

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Planck constant Often, when describing things oscillating, it is more useful to work in terms of angular frequency instead of frequency f This ratio comes up so often, it is given its own name and symbol. It is called the reduced Planck constant, and is read as h-bar Units of Planck constant h and h-bar have units of kg*m^2/s – same as angular momentum

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Photoelectric Effect: Hertz, 1887 Metal is hit by light Electrons pop off Must exceed minimum frequency Depends on the metal Brighter light, more electrons They start coming off immediately Even in low intensity Metal e-e- e-e- e-e- e-e- Einstein, 1905 It takes a minimum amount of energy to free an electron Light really comes in chunks of energy hf If hf < , the light cannot release any electrons from the metal If hf > , the light can liberate electrons The energy of each electron released will be E kin = hf –

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Photoelectric Effect Will the electron pass through a charged plate that repels electrons? Must have enough energy Makes it if: Metal e-e- +––+ V f V max slope = h/e Nobel Prize, 1921

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Sample Problem When ultraviolet light of wavelength 227 nm strikes calcium metal, electrons are observed to come off which can penetrate a barrier of potential up to V max = 2.57 V. 1.What is the work function for calcium? 2.What is the longest wavelength that can free electrons from calcium? 3.If light of wavelength 312 nm were used instead, what would be the energy of the emitted electrons? We need the frequency: Continued...

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Sample Problem continued 2.What is the longest wavelength that can free electrons from calcium? 3.If light of wavelength 312 nm were used instead, what would be the energy of the emitted electrons? The lowest frequency comes from V max = 0 Now we get the wavelength: Need frequency for last part:

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X-rays Mysterious rays were discovered by Röntgen in 1895 Suspected to be short-wavelength EM waves Order 1-0.1 nm wavelength Scattered very weakly off of atoms Bragg, 1912, measured wavelength accurately dd dcos Scattering strong only if waves are in phase Must be integer multiple of wavelength

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Atom The Compton Effect By 1920’s X-rays were clearly light waves 1922 Arthur Compton showed they carried momentum e-e- e-e- e-e- Photon in Photon out Conservation of momentum and energy implies a change in wavelength Meanwhile... Photons carry energy and momentum, just like any other particle

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Early Quantum Theory and Models of the Atom

Early Quantum Theory and Models of the Atom

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