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UW-Madison PHYSICS 107 - PHYSICS 107 Lecture Notes

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From Last Time…Energy LevelsEnergy Levels in a Metaln- and p-type semiconductorsJunctionsLight emitting diodeElectrical resistanceResistance questionLife is toughTemperature-dependent resistanceResistanceWhy does temperature matter?Temperature scalesWhat happens at the lowest temperature?Sometimes, something else!SuperconductivityPersistent currentsCritical currentSuperconducting elementsCritical temperaturesHigher transition temperaturesMeissner effectSlide 23PowerPoint PresentationSlide 25Slide 26QuestionCritical magnetic fieldCritical fieldsA century of superconductivitySlide 31Superconducting power cablesSuperconducting MagnetsMagnetic LevitationSuperconducting TrainTevatronPhy107 Fall 20061From Last Time…Today•Conductors and superconductors•Molecules–Symmetric and anti-symmetric wave functions–Lightly higher and lower energy levels–More atoms more energy levels•Conductors, insulators and semiconductorsDue Friday: Essay outlineHW9: Chap 15 Conceptual: # 2, 4, 14, 24 Problems: # 2, 4Phy107 Fall 20062Energy Levels•Basic n levels, •include l and mlZero energyn=1n=2n=3n=4€ E1= −13.612 eV€ E2= −13.622 eV€ E3= −13.632 eVEnergy axisPhy107 Fall 20063Energy Levels in a Metal1s2s3s2p3pNa = [Ne]3s1empty1 electron6 electrons2 electrons2 electronsFullFullFull3p3s2p2s1sPartially FullThis band not completely occupied•Include molecular symmetric and anti-symmetric wavefuctionsPhy107 Fall 20064n- and p-type semiconductorsElectrons from donorsn-type semiconductorDonors, one extra electron‘Holes’ from acceptorsp-type semiconductorAcceptors, one fewer electronPhy107 Fall 20065Junctions•Real usefulness comes from combining n and p-type semiconductorsn-type p-typeJunction develops a ‘built-in’ electric field at the interface due to charge rearrangement.Phy107 Fall 20066Light emitting diode•Battery causes electrons and holes to flow toward pn interface•Electrons and holes recombineat interface (electron drops down to lower level)•Photon carries away released energy.•Low energy use - one color!Phy107 Fall 20067Electrical resistance•Last time we said that a metal can conduct electricity. •Electrons can flow through the wire when pushed by a battery.•But remember that the wire is made of atoms.•Electrons as waves drift through the atomic lattice.Phy107 Fall 20068Resistance questionSuppose we have a perfect crystal of metal in which we produce an electric current. The electrons in the metalA.Collide with the atoms, causing electrical resistanceB.Twist between atoms, causing electrical resistanceC.Propagate through the crystal without any electrical resistanceIf all atoms are perfectly in place, the electron moves though the without any resistance!Phy107 Fall 20069Life is tough•In the real world, electrons don’t have it so easySome missing atoms (defects)Vibrating atoms!Electron scatters from these irregularities, -> resistancePhy107 Fall 200610Temperature-dependent resistanceSuppose we cool down the wire that carries electrical current to light bulb. The light willA.Get brighterB.Get dimmerC.Stay samePhy107 Fall 200611Resistance•As elecron wave propagates through lattice, it faces resistance•Resistance:Bumps from vibrating atomsCollisions with impuritiesRepulsion from other electrons•Electrons ‘scatter’ from these atomic vibrations and defects.•Vibrations are less at low temperature, so resistance decreases. •More current flows through wire•Life is tough for electrons, especially on hot dayshttp://regentsprep.org/Regents/physics/phys03/bresist/default.htmPhy107 Fall 200612Why does temperature matter?Temperature is related to the energy of a macroscopic object.•The energy usually shows up as energy of random motion.•There really is a coldest temperature, corresponding to zero motional energy!•The Kelvin scale has the same size degree as the Celsius (˚C) scale. But 0 K means no internal kinetic energy. •0 degrees Kelvin (Absolute Zero) is the coldest temperature possible–This is -459.67 ˚FPhy107 Fall 200613Temperature scales•Kelvin (K):–K = C + 273.15–K = 5/9 F + 255.37FahrenheitCelsius Kelvin comments212 100 373.15water boils32 0 273.15water freezes-300.42 -195.79 77.36liquid nitrogen boils-452.11 -268.95 4.2liquid helium boils-459.67 -273.15 0absolute zeroPhy107 Fall 200614What happens at the lowest temperature?Kelvin (1824-1907): electrons freeze and resistance increases Onnes (1853-1926): Resistance continues drop, finally reaching zero at zero temperaturePhy107 Fall 200615Heike Kamerlingh Onnes •1908 - liquefied helium (~4 K = - 452°F )•1911- investigated low temperature resistance of mercury•Found resistance dropped abruptly to zero at 4.2 K•1913 - Nobel Prize in physicsSometimes, something else!Phy107 Fall 200616Superconductivity•Superconductors are materials that have exactly zero electrical resistance.•But this only occurs at temperatures below a critical temperature, Tc•In most cases this temperature is far below room temperature.Hg (mercury)Not superconducting (normal)SuperconductingCritical TemperaturePhy107 Fall 200617Persistent currents•How zero is zero?•EXACTLY!•Can set up a persistent current in a ring.•The magnitude of the current measured by the magnetic field generated.•No current decay detected over many years!Persistent supercurrentMagnetic fieldPhy107 Fall 200618Critical current•If the current is too big, superconductivity is destroyed.•Maximum current for zero resistance is called the critical current.•For larger currents, the voltage is no longer zero, and power is dissipated.CurrentVoltageCritical currentNot superconducting (normal)SuperconductingCritical CurrentPhy107 Fall 200619Superconducting elements•Many elements are in fact superconducting•In fact, most of them are!Phy107 Fall 200620Critical temperaturesIf superconductivity is so common, why don’t we have superconducting cars, trains, toothbrushes?Many superconducting critical temperatures are low.Element Critical T. (K)(˚C) (˚F)Aluminum 1.75 -271 -457Mercury 4.15 -269 -452Lead 7.2 -266 -447Tin 3.72 -269 -453Niobium 9.25 -264 -443Phy107 Fall 200621Higher transition temperatures•Much higher critical temperature alloys have been discovered•NbTi 10 K•Nb3Sn 19 K•YBa2Cu3O7, 92 K•BiSrCaCuO, 120 KHigh-temperature superconductorsPhy107 Fall 200622Meissner effect•Response to magnetic field•For small magnetic fields a superconductor will spontaneously expel all magnetic


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UW-Madison PHYSICS 107 - PHYSICS 107 Lecture Notes

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