* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download in nm 1240 E in eV - Little Shop of Physics
Molecular Hamiltonian wikipedia , lookup
Tight binding wikipedia , lookup
Bremsstrahlung wikipedia , lookup
Renormalization wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Delayed choice quantum eraser wikipedia , lookup
Atomic orbital wikipedia , lookup
Elementary particle wikipedia , lookup
Wheeler's delayed choice experiment wikipedia , lookup
Ferromagnetism wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Ultraviolet–visible spectroscopy wikipedia , lookup
X-ray photoelectron spectroscopy wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Particle in a box wikipedia , lookup
Electron configuration wikipedia , lookup
Ultrafast laser spectroscopy wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Atomic theory wikipedia , lookup
Double-slit experiment wikipedia , lookup
Matter wave wikipedia , lookup
Wave–particle duality wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Quantum Mechanics • Light has a particle nature. This is most clearly shown by the photoelectric effect. • Particles have a wave nature. All of the wave phenomena we have seen apply to particles as well. • Quantum principles are well understood and well accepted. But they are pretty weird. 1 The photon model 1240 ! (in nm) 1240 ! ( in nm ) = E ( in eV) E (in eV) = First example of quantization. 2 Creating X rays If an electron is accelerated through a 5.0 kV potential difference, what is the maximum photon energy of the resulting x ray? What is the wavelength? One electron. One photon. 3 Photon Production A particular species of bioluminescent copepod (a small marine crustacean, typically a few mm in length) emits blue light at a peak wavelength of 490 nm. In a typical flash lasting 2.4 s, the copepod emits 1.4 x 1010 photons. • What power does this correspond to? • What is the intensity at a distance of 10 m? hc ! h = 6.62 " 10 #34 J $s Ephoton = P = !E !t I = Psource 4" r 2 4 Can You See a Single Photon? At the wavelength corresponding to the maximum sensitivity of the human eye, 510 nm, the limit of sensitivity of the darkadapted eye has been shown to be correspond to a 100 ms flash of light of total energy 240 eV. (Weaker flashes of light may be detected, but not reliably.) Problems 837 es ec- gh he ith lly tiarhe he as a ce of his ter ny ogy a) What is the energy of a single photon at this wavelength? 52. How | Ourmany sun’sphotons 5800 K surface temperature gives a peak waveb) does the flash contain? length in the middle of the visible spectrum. What is the mini- c) Ifmum 60%surface of the temperature incident light to reflection for isa lost star whose emissionand peaks at absorption by tissues of 400 the nm—that eye, howis,many reach some wavelength less than in thephotons ultraviolet? 53. the ||| While using a dimmer switch to investigate a new type of retina? incandescent light bulb, you notice that the light changes both The light from the flash covers well over 500 rod cells. its spectral characteristics and its brightness as the voltage is increased. d) So, can you see a single photon? a. If the wavelength of maximum intensity decreases from 1800 nm to 1600 nm as the bulb’s voltage is increased, by how many does the filament temperature increase? b. By what factor does the total radiation from the filament increase due to this temperature change? 54. || The star Sirius is much hotter than the sun, with a peak wavelength of 290 nm compared to the sun’s 500 nm. It is also larger, with a diameter 1.7 times that of the sun. By what factor does the energy emitted by Sirius exceed that of the sun? 55. | The photon energies used in different types of medical x-ray imaging vary widely, depending upon the application. Single dental x rays use photons with energies of about 25 keV. The photon energy used for x-ray microtomography, a process that allows repeated imaging in single planes at varying depths within the sample, is 2.5 times greater. What are the wavelengths of the x rays used for these two purposes? Ratios. 56. | A python can detect thermal radiation with intensity greater than 0.60 W/m2. A typical human body has a surface area of 1.8 m2, a surface temperature of 30°C, and an emissivity at infrared wavelengths. What is the maximum distance from which a python can detect your presence? You can model the human body as a point source of radiation. 57. | If astronomers look toward any point in outer space, they see 5 6 vity m2, 5.65 of ire? ent? polarizer with axis from vertical is inserted between the first two. What is the transmitted intensity now? 72. ||| A light-emitting diode (LED) connected to a 3.0 V power supply emits 440 nm blue light. The current in the LED is 10 mA, and the LED is 60% efficient at converting electric power input into light power output. How many photons per second does the LED emit? 73. | A 1000 kHz AM radio station broadcasts with a power of 20 kW.you Howhad manytophotons emit What pay does the transmitting Whatantenna you get each second? 74. |||| The human body has a surface area of approximately a surface temperature of approximately 30°C, and a typical emissivity at infrared wavelengths of If we make the approximation that all photons are emitted at the wavelength of peak intensity, how many photons per second does the body emit? meter MCAT-Style Passage Problems Electromagnetic Wave Penetration Radio waves and microwaves are used in therapy to provide “deep heating” of tissue because the waves penetrate beneath the surface of the body and deposit energy. We define the penetration depth as the 7 Quantum Concept #1: EM Waves have a particle nature 16/10/13 9:49 AM 8 The Photoelectric Effect Light Window I Ammeter Cathode Anode A f DV I 0 f0 There is a threshold frequency. Above it, electrons are emitted. Below it, not so much. 9 Just Checking In the photoelectric effect experiment, why does red light not cause the emission of an electron though blue light can? The photons of red light don’t have sufficient energy to eject an electron. Red light contains fewer photons than blue, not enough to eject electrons. The electric field of the red light oscillates too slowly to eject an electron. The red light doesn’t penetrate far enough into the metal electrode. 10 The Photoelectric Effect Light Window I Intense light Weak light Ammeter Cathode Anode A DV 2Vstop 0 I DV Changing the accelerating voltage changes the current. But only within certain limits. 11 Just Checking In the photoelectric effect experiment, increasing the accelerating voltage from 3.0 V to 5.0 V does not increase the current. How can we explain this result? The resistance of the tube changes as well. The electrons are already at their maximum speed. 3.0 V makes all the electrons reach the anode, so increasing voltage causes no change. Increasing the voltage doesn’t change the electron kinetic energy. 12 takes more than the ugh to escape. minimum energy. k function of The Work Function e more energy work functions How much it “costs” to release an electron. 60 * 10-19 J.) This varies with the electrode. e 28.6. When TABLE 28.1 The work functions tic energy. An for some metals , so it emerges Element E0 (eV) n energy E0 is Potassium 2.30 ossible kinetic ns. FIGURE 28.9 and the anode = 0, there will e anode, creat- Sodium 2.75 Aluminum 4.28 Tungsten 4.55 Copper 4.65 Iron 4.70 Gold 5.10 13 ode. A further e and thus does Think It. n Figure 28.7bAbout FIGURE 28.9 The effect of different eaving the catha ball hits the negative anode ecreases as the of Figure 28.7b current ceases. voltages between Lightthe anode and cathode. Window UV Ammeter Cathode Anode A Cathode Anode ∆V = 0: The electrons leave the cathode in all directions. Only some reach the anode. energy to the f Figure 28.9, I DV energy as they e for electrons 5.0 eV photons strike an electrode with work function 3.0 eV. nergy. When What with Ka.max , are is the kinetic energy of emitted electrons? 100%b.ofWhat their potential is needed to reduce the current to zero? Kmax , or (28.2) 14 ∆V 7 0: Making the anode positive creates an electric field that pushes all the electrons to the anode. Just Checking. imum kinetic Monochromatic light shines on the cathode in a photoelectric effect experiment, causing the emission of electrons. If the intensity of the light stays the hy dosame electrons but the frequency of the light is increased, ed on classical rons, so it was the ∆V emitted electrons 6 0: Making the anode negative repels the , causing it to electrons. Only the a very fastest make it to the both A and will be moving at nt. For light to anode. B are true. higher speed. there will be more electrons emitted. neither A nor B are 24/10/13 1:57true. PM 15 Just Checking. Monochromatic light shines on the cathode in a photoelectric effect experiment, causing the emission of electrons. If the frequency of the light stays the same but the intensity of the light is increased, the emitted electrons will be moving at a higher speed. both A and B are true. there will be more electrons emitted. neither A nor B are true. 16 The Details. Light of wavelength 400 nm illuminates a potassium electrode (work function 2.3 eV). a. What is the photon energy? b. What is the energy of the emitted electron? c. What is the stopping potential? Light Window! Ammeter Cathode !! ! DV! Anode A I 17 Metal surfaces on spacecraft in bright sunlight develop a net electric charge. Do they develop a negative or a positive charge? Explain. What’s The Fizics? 18 Diffraction and Interference 19 Diffraction Diffraction and Interference 20 Double Slit Interference Pattern Viewing screen Incident laser beam Longer wavelength means bigger spacing. 21 Grating Interference Pattern Screen y y2 m52 y1 m51 0 m50 2y1 m51 2y2 m52 Grating u2 u1 Dr between these paths is exactly 2l (m 5 2). Appearance of screen L 22 Particles have a Wave Nature != h h = p mv De Broglie wavelength for a moving particle 23 Particle or Wave? m ! Localized. Smeared out. Wavelength of a squirrel running at 3 m/s: 1x10-33 m 24 Particle or Wave? In a television set, an electron is accelerated by a voltage of 150 V. a. What is the kinetic energy of the electron? b. What is the speed of the electron? c. What is the De Broglie wavelength? Does this matter? Size of a hydrogen atom Orbitals 0.1 nm 25 Looking Deeper Electron microscope view of pigment molecule. 26 Quantum Concept #3: The wave nature of particles leads to quantization. 27 Particles have a wave nature. So... Particle: L m v Wave: L ...the possible states are quantized. 28 The Crux of the Quantum Biscuit Photons have a particle nature. Their energy is quantized. It comes in chunks of a particular size. Particles have a wave nature. Confining them restricts them to certain energy states. The energy of a confined particle is quantized. It is restricted to certain values. 29 The wave nature of particles leads to quantized energy levels for electrons in atoms. Only certain transitions are possible. Energy Energy 160 eV n54 90 eV n53 n54 160 eV 90 eV 40 eV n52 40 eV 10 eV 0 n51 10 eV 0 DEsystem 5 |E3 2 E1| 5 80 eV DEsystem 5 |E1 2 E2| 5 30 eV n53 n52 n51 Ground state Energy levels for a particle in a 0.10-nm-long box Possible transitions for a system with these energy levels 2 En = 1 ! hn $ h2 2 = n 8mL2 2m #" 2L &% n = 1, 2, 3, 4... 30 What is the maximum photon energy that could be emitted by the quantum system with the energy level diagram shown below? The minimum? 31 The Details. Light of wavelength 400 nm illuminates a potassium electrode (work function 2.3 eV). a. What is the photon energy? b. What is the energy of the emitted electron? c. What is the stopping potential? Light Window! Ammeter Cathode !! ! DV! Anode A I Ocean water is most transparent at wavelengths of 470 nm, so bioluminescent creatures emit light at approximately this wavelength. Firefly squid use ATP to provide the energy for this reaction. Metabolizing one molecule of ATP releases 0.32 eV. How many molecules of ATP must be metabolized to produce one photon of blue light at 470 nm? 32 33 In a photoelectric effect experiment, light of wavelength 620 nm shines on a cathode with a work function of 1.8 eV. • What is the speed of the emitted electron? • What anode voltage will stop current in the tube? 34 Electrons are accelerated from rest through an 8000 V potential difference. By what factor would their de Broglie wavelength increase if they were instead accelerated through a 2000 V potential? K = !U e Electron moving more slowly: K = 12 mv 2 Wavelength is longer. != h h = p mv Ratio reasoning. 35 The wave nature of particles leads to quantization. L m v L 2 1 ! hn $ h2 2 En = = n 8mL2 2m #" 2L &% n = 1, 2, 3, 4... Allowed energies for particle in a box 36 The wave nature of particles leads to quantized energy levels for electrons in atoms. Only certain transitions are possible. Energy 160 eV 90 eV Energy n54 n53 n54 160 eV 90 eV 40 eV n52 40 eV 10 eV 0 n51 10 eV 0 DEsystem 5 |E3 2 E1| 5 80 eV DEsystem 5 |E1 2 E2| 5 30 eV n53 n52 n51 Ground state Energy levels for a particle in a 0.19-nm-long box Possible transitions for a system with these energy levels 37 What energy photons could be emitted by the quantum system sketched below? 38 Electrons of the bonds along the chain of carbon atoms in this dye molecule are shared among the atoms in the chain, but are repelled by the nitrogen-containing rings at the end of the chain. What is the longest wavelength of visible light this molecule will absorb? 0.85 nm 39 If the length of the chain is increased, how will this affect the wavelength of the light absorbed by the dye? Ratio reasoning. 2 1 ! hn $ h2 2 En = = n 2m #" 2L &% 8mL mL2 mL n = 1, 2, 3, 4... 40 Changing Scale The diameter of a typical atomic nucleus is about 10 fm. (1 fm is 1x10-15 m.) What is the kinetic energy, in MeV, of a proton with a de Broglie wavelength of 10 fm? 41 Heisenberg uncertainty principle ∆ x ∆p px ⁄ h 4p !x 42 Uncertainty If I know where you are, I don’t know where you are going. !v " "x large 1 !x "x small 43 Electrons & Atoms An electron is associated with a particular atom. This limits it to an uncertainty in position of about 1 nm—it’s somewhere within this range. What uncertainty in speed does this imply? 44 “Beaming” Someone... 45 A spherical virus has a diameter of 50 nm. It is contained wavesinside obey the principle of superposition and 0.0001 exhibit interference. This a long, narrow cell of length m. particle dichotomy seemed obvious until physicists encountered irrefutable What uncertainty imply velocity the ce that light sometimes actsdoes like a this particle and,for eventhe stranger, that of matter virus mes acts likealong a wave.the length of the cell? Assume the virus has a might at first are both a wave and a particle, but density think equalthattolight thatandofmatter water. a doesn’t quite work. The basic definitions of particleness and waviness are ly exclusive. Two sound waves can pass through each other and can overlap uce a larger-amplitude sound wave; two baseballs can’t. It is more profitable lude that light and matter are neither a wave nor a particle. At the microscale of atoms and their constituents—a physical scale not directly accessible ive senses—the classical concepts of particles and waves turn out to be simlimited to explain the subtleties of nature. ough matter and light have both wave-like aspects and particle-like aspects, ow us only one face at a time. If we arrange an experiment to measure a ke property, such as interference, we find photons and electrons acting like not particles. An experiment to look for particles will find photons and eleccting like particles, not waves. These two aspects of light and matter are mentary to each other, like a two-piece jigsaw puzzle. Neither the wave nor ticle model alone provides an adequate picture of light or matter, but taken r they provide us with a basis for understanding these elusive but most fundaconstituents of nature. This two-sided point of view is called wave–particle 46 Heisenberg uncertainty principle over two hundred years, scientists and nonscientists alike felt that the clockniverse of Newtonian physics was a fundamental description of reality. But particle duality, along with Einstein’s relativity, undermines the basic assumpf the Newtonian worldview. The certainty and predictability of classical have given way to a new understanding of the universe in which chance and inty play key roles—the universe of quantum physics. 2 h 2# E = mc !E!t " ual nature of a buckyball Treating atomic-level structures involves frequent ween particle and wave views. 60 carbon atoms can create the molecule med at left, known as C60, or buckminsterfullerene. The scanning electron ope image of a C60 molecule shown on the right is a particle-like view of the e with individual carbon atoms clearly visible. The C60 molecule, though we e a picture of it—showing the atoms that make it up—also has a wave nature. A C60 sent through a grating will produce a diffraction pattern! nance imaging manent magt of electrons ons also have for magnetic 47 where m = 1.41 * 10-26 J/T is the known value of the proton’s magnetic moment. FIGURE 28.25 shows the two possible energy states. The magnetic moment, like a compass needle, “wants” to align with the field, so that is the lower-energy state. But a quantum compass is different. FIGURE 28.25 Energy levels for a proton in a magnetic field. align with a on. This isn’t ntum physics There are only orientations— Quantum mechanics limits the proton to two possible energies . . . . . . which correspond to two possible orientations, aligned with or opposite the magnetic field. Energy E2 5 1mB field e the field r B 0 E1 5 2mB µproton = 1.41! 10 "26 J/T • What is the photon energy corresponding to a spin flip • • for a proton in a 1.0 T magnetic field? What frequency does this correspond to? What type of EM wave is this? 48 ons also have for magnetic states. The magnetic moment, like a compass needle, “wants” to align with the field, so that is the lower-energy state. Changing field, changing frequency. FIGURE 28.25 Energy levels for a proton in a magnetic field. align with a on. This isn’t ntum physics There are only orientations— Quantum mechanics limits the proton to two possible energies . . . . . . which correspond to two possible orientations, aligned with or opposite the magnetic field. Energy r B E2 5 1mB field e the field 0 E1 5 2mB µproton = 1.41! 10 "26 J/T If you increase the field from 1.0 T to 2.0 T, how does this change the frequency of the rf (radiofrequency) wave necessary to cause a spin flip? 49 Quantum Weirdness: Non-locality Two places at one time Which slit did the electron go through? Where is the electron? 50 Quantum Weirdness: Superposition Many things in the same place 51 Quantum Weirdness: Mixed States Alive and dead cats Schrödinger’s Cat 52 Fluorescence A range of wavelengths can excite electrons to the upper band. The electrons fall to the lower edge of the upper band. The electrons then jump to the lower band, emitting photons. Would you expect the absorbed or the emitted light to have a longer wavelength? 53 Relative intensity Absorption band Emission band 0 300 400 500 600 Wavelength (nm) 54