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Download Presentation Lesson 27 Quantum Physics
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Lesson 27 Quantum Physics Eleanor Roosevelt High School Chin-Sung Lin The Model of Atom The Planetary Model of Atom • Niels Bohr’s model • Positive charge is in the center of the atom (nucleus ) • Atom has zero net charge • Electrons orbit the nucleus like planets orbit the sun • Attractive Coulomb force plays role of gravity The Planetary Model of Atom • Circular motion of orbiting electrons causes them to emit electromagnetic radiation with frequency equal to orbital frequency, and carries away energy from the electron – Electron predicted to continually lose energy – The electron would eventually spiral into the nucleus However most atoms are stable! The Planetary Model of Atom • Experimentally, atoms do emit electromagnetic radiation, but not just any radiation! • Each atom has its own ‘fingerprint’ of different light frequencies that it emits 400 nm 500 nm 600 nm 700 nm Hydrogen Mercury Wavelength (nm) The Planetary Model of Atom • The Balmer Series of emission lines empirically given by n=4 Rydberg constant : RH = 1.097 ´ 10 7 m -1 n = 4, = 486.1 nm n = 3, = 656.3 nm Hydrogen n=3 The Planetary Model of Atom • One electron orbits around one proton and only certain orbits are stable • Radiation emitted only when electron jumps from one stable orbit to another • Here, the emitted photon has an energy of E initial – E final Einitial Photon Efinal The Planetary Model of Atom • Hydrogen emits only photons of a particular wavelength, frequency • Photon energy = hf, so this means a particular energy The Planetary Model of Atom • Energy is quantized n=4 n=3 E3 = - 13.6 eV 32 n=2 E2 = - 13.6 eV 22 n=1 E1 = - 13.6 eV 12 Energy axis Zero energy The Planetary Model of Atom Zero energy n=4 n=3 13.6 E 3 = - 2 eV 3 n=2 E2 = - 13.6 eV 22 Photon emitted hf=E2-E1 n=4 n=3 E3 = - 13.6 eV 32 n=2 E2 = - 13.6 eV 22 E1 = - 13.6 eV 12 Photon absorbed hf=E2-E1 n=1 E1 = - 13.6 eV 12 Photon is emitted when electron drops from one quantum state to another n=1 Absorbing a photon of correct energy makes electron jump to higher quantum state. The Planetary Model of Atom • A useful model of the atom must be consistent with a model for light, for most of what we know about atoms we learn from the light and other radiations they emit • Most light has its source in the motion of electrons within the atom Models of Light The Model of Light • Two primary models of light: the particle model and the wave model The Model of Light • Isaac Newton believed in a particle model of light • Christian Huygens believed that light was a wave • Thomas Young demonstrated the wave property of light – Interference • James Clerk Maxwell proposed that light is a part of broader electromagnetic wave spectrum • Heinrich Hertz produced radio wave as Maxwell’s prediction • Albert Einstein resurrected the particle theory of light Light Quanta • Max Planck believed that light existed as continuous waves. However, he proposed that atoms emit and absorb light in little chunks – quanta (pl. of quantum) • Einstein further proposed that light itself is composed of quanta (now called photons) • A quantum is an elementary unit (smallest amount) of something • Mass, electric charge, light, energy, and angular momentum are all quantized • Only a whole number of quanta can exist Light Quanta • Photons have no rest energy • Photons move at speed of light • The energy of a photon is its kinetic energy (E) • The photon’s energy is directly proportional to its frequency • E = hf (h is Planck’s constant) is the smallest amount of energy that can be converted to light of frequency f • Light is a stream of photons, each with an energy hf Photoelectric Effect Photoelectric Effect • The photoelectric effect refers to the emission of electrons from the surface of a metal in response to incident light • Energy is absorbed by electrons within the metal, giving the electrons sufficient energy to be 'knocked' out of the surface of the metal Photoelectric Effect • Maxwell wave theory of light predicts that the more intense the incident light the greater the average energy carried by an ejected (photoelectric) electron • Experiment shows that the energies of the emitted electrons to be independent of the intensity of the incident radiation • Einstein (1905) resolved this paradox by proposing that the incident light consisted of individual quanta, called photons, that interacted with the electrons in the metal like discrete particles, rather than as continuous waves Photoelectric Effect • For a given frequency of the incident radiation, each photon carried the energy E = hf, where h is Planck's constant and f is the frequency Photoelectric Effect • Light travels as a wave • Light interacts with matter as a stream of particles Waves vs. Particles Waves vs. Particles • Images made by a digital camera. In each successive image, the dim spot of light has been made even dimmer by inserting semitransparent absorbers like the tinted plastic used in sunglasses Waves vs. Particles • Which model can explain the phenomenon? Waves vs. Particles • If light was a wave, then the absorbers would simply cut down the wave's amplitude across the whole wavefront • The digital camera's entire chip would be illuminated uniformly • But figures show that some pixels take strong hits while others pick up no energy at all • Instead of the wave picture, the image that is naturally evoked by the data is something more like a hail of bullets from a machine gun • Each "bullet" of light apparently carries only a tiny amount of energy – light is consist of a stream of particles Waves vs. Particles Electron beam is directed toward a crystal Waves vs. Particles Diffraction & interference pattern is observed Waves vs. Particles • The behavior of a particle of matter (in this case the incident electron) can be described by a wave • Electrons behave like a wave! Waves vs. Particles • If waves can have particle properties, cannot particles have wave property? • De Broglie answered this question in 1924 • He suggested that all matter (electrons, protons, atoms, marbles, cars, and even human) have wave properties • This phenomenon is commonly known as the waveparticle duality Waves vs. Particles • If waves can have particle properties, cannot particles have wave property? • De Broglie answered this question in 1924 • He suggested that all matter (electrons, protons, atoms, marbles, cars, and even human) have wave properties • This phenomenon is commonly known as the waveparticle duality Material Waves Material Waves • All matter have wave properties • The wavelength of a particle is called the de Broglie wavelength • A tiny particle moving at typical speed has a detectable wavelength • Objects in our daily life have tiny wavelengths which are beyond detection Wavelength of an Electron • Need less massive object to show wave effects • Electron is a very light particle • Mass of electron = 9.1x10-31 kg • Larger velocity, shorter wavelength • Wavelength depends on mass and velocity Wavelength of a Football Example: A football’s weight is 0.4 kg and the speed is 30 m/s. Calculate the wavelength of the football Momentum: mv = (0.4 kg)( 30 m /s) =12 kg · m /s Material Waves • Example: Calculate the de Broglie wavelength of an electron traveling at 2% the speed of light Material Waves • Example: Calculate the de Broglie wavelength of an ball traveling at 330 m/s Material Waves • A beam of electrons behaves like a beam of light, however, the wavelength is typically thousands of times shorter than the wavelength of the visible light Material Waves • The electron microscope can distinguish detail not possible with optical microscopes Electron Waves • The Bohr’s model explained the spectra of the element. It explained why elements emitted only certain frequencies of light since electrons can only transfer among certain energy levels • The model failed to explain why electrons only occupied certain energy levels I the atom • Bohr showed that in such a model the electrons would spiral into the nucleus in about 10-10 s, due to electrostatic attraction • This can be resolved by viewing electrons as waves instead of particles Electron Waves • In 1923, de Broglie, proposed that a way to explain the discrete energy levels was that electrons behave like waves • To ‘fit a wave’ around a nucleus is when the wavelength fits the circumference a whole-number of times (so called standing waves ), and these states correspond to the observed energy levels of the electrons Electron Waves • The radius of a ground state, n = 1, electron has a circumference of one standing wave • The radius of the first excited state, n = 2, has a circumference of two standing waves Electron Waves • Thus, an electron's orbit cannot decay because it is constrained by its standing wave forms • Only those radii whose circumferences equaled a multiple of the electron's de Broglie wavelength were permitted Electron Waves • De Broglie’s predictions for the electron orbits were quickly confirmed by experiment and were found to perfectly fit the observed energy levels of electrons in atoms • De Broglie thus created a new field in physics, the wave mechanics, uniting the physics of energy (wave) and matter (particle). For this he won the Nobel Prize in Physics in 1929 Relative Sizes of Atoms Relative Sizes of Atoms • The radii of the electron orbits in the Bohr’s atomic model are determined by the amount of electric charge in the nucleus • As the positive charge in the nucleus increased, the negative electrons also increased. The inner orbits shrink in size due to stronger electric attraction. However, it won’t shrink as much as expected due to the increasing electrons • The heavier elements are not much larger in diameter than the lighter elements • Each element has unique arrangement of electron orbits unique to that element Relative Sizes of Atoms Atomic Energy Levels & Photon Energy 47 Bohr’s Atomic Model • Electron orbits around the nucleus and only certain orbits are stable • Radiation emitted only when electron jumps from one stable orbit to another Photon Ephoton Einitial Efinal • The emitted photon has an energy E photon = E initial – E final 48 Quantized Energy Levels • Energy level diagrams on page 3 of your reference table 49 Quantized Energy Levels • Each atom has a set of discrete energy levels • Each level has been assigned a quantum number (n) • An electron transits in hydrogen between quantized energy levels 50 Quantized Energy Levels • How many different transitions to the lower energy levels can an electron have when the electron is at n = 4? 51 Quantized Energy Levels • How many different transitions to the lower energy levels can an electron have when the electron is at n = 4? 3 different transitions: n = 4 —> n = 3 n = 4 —> n = 2 n = 4 —> n = 1 52 Quantized Energy Levels • How many different transitions to the lower energy levels can an electron have when the electron is at n = 7 ? 53 Quantized Energy Levels • How many different transitions to the lower energy levels can an electron have when the electron is at n = 7 ? 6 different transitions 54 Energy of Photons • Calculate the energy of photons for those possible transitions form n = 4 55 Energy of Photons • Calculate the energy of photons for those possible transitions form n = 4 3 possible transitions: n = 4 —> n = 3 -0.85 eV – (-1.51 eV) = 0.66 eV n = 4 —> n = 2 -0.85 eV – (-3.40 eV) = 2.55 eV n = 4 —> n = 1 -0.85 eV – (-13.6 eV) = 12.75 eV 56 Quantized Energy Levels • How much energy is required to ionize the Hydrogen atom? 57 Quantized Energy Levels • How much energy is required to ionize the Hydrogen atom? E > 13.6 eV 58 Electronvolts & Joules • The electronvolt (eV) is a unit of energy • It is the kinetic energy gained by an electron when it accelerates through an electric potential difference of 1 volt • Since V = W/q, or W = qV, for a single electron 1 eV = 1.602×10−19 C x 1 V ( or 1 J/C) = 1.602×10−19 J 1 eV = 1.60 × 10−19 J 59 Energy of Photons • Calculate the energy of photons for the transitions form n = 4 to n = 2 in joules 60 Energy of Photons • Calculate the energy of photons for the transitions form n = 4 to n = 2 in joules n = 4 —> n = 2 -0.85 eV – (-3.40 eV) = 2.55 eV = 2.55 eV x 1.6 x 10 -19 J/eV = 4.08 x 10 -19 J 61 Quantized Energy Levels • How much energy (in joules) is required to ionize the Hydrogen atom? 62 Quantized Energy Levels • How much energy (in joules) is required to ionize the Hydrogen atom? E > 13.6 eV E > 13.6 eV x 1.6 x 10 -19 J/eV E > 2.18 x 10 -18 J 63 Electron Transition • Hydrogen emits only photons of particular energies • The emitted photon has an energy E photon = E initial – E final 64 Atomic Spectrum • Hydrogen emits only photons of a set of particular energy • Photon energy E = hf = hc/λ (h = 6.63 × 10–34 J•s) • It emits a set of particular wavelengths, and frequencies 65 Atomic Spectrum Zero energy n=4 n=3 13.6 E 3 = - 2 eV 3 n=2 E2 = - 13.6 eV 22 Photon emitted hf=E2-E1 n=4 n=3 E3 = - 13.6 eV 32 n=2 E2 = - 13.6 eV 22 E1 = - 13.6 eV 12 Photon absorbed hf=E2-E1 n=1 E1 = - 13.6 eV 12 Photon is emitted when electron drops from one quantum state to another n=1 Absorbing a photon of correct energy makes electron jump to higher quantum state. 66 Electron Transition • E photon = E initial – E final • E photon = h f = h c / λ • The emitted photon has a frequency and wavelength: f = E photon / h λ = h c / E photon h = 6.63 × 10–34 J•s (Plank’s constant) 67 Frequency of Photons • Calculate the frequency of photons for the transitions form n = 4 to n = 2 in a hydrogen atom 68 Frequency of Photons • Calculate the frequency of photons for the transitions form n = 4 to n = 2 in a hydrogen atom E photon = E initial – E final = -0.85 eV – (-3.40 eV) = 2.55 eV = 2.55 eV x 1.6 x 10 -19 J/eV = 4.08 x 10 -19 J f=E/h = 4.08 x 10 -19 J / 6.63 × 10–34 J•s = 6.15 x 10 14 Hz 69 Wavelength of Photons • Calculate the wavelength of photons for the transitions form n = 4 to n = 2 in a hydrogen atom 70 Wavelength of Photons • Calculate the wavelength of photons for the transitions form n = 4 to n = 2 in a hydrogen atom E photon = E initial – E final = 4.08 x 10 -19 J λ = h c / E photon = (6.63 × 10 –34 J•s) (3.00 x 10 8 m/s) / 4.08 x 10 -19 J = 4.88 x 10 –7 m 71 Type of Photons • Identify the type of photons for the transitions form n = 4 to n = 2 in a hydrogen atom 72 Type of Photons • Identify the type of photons for the transitions form n = 4 to n = 2 in a hydrogen atom E photon = E initial – E final = 4.08 x 10 -19 J f = E / h = 6.15 x 10 14 Hz 73 Electromagnetic Spectrum • Electromagnetic spectrum diagram on page 2 of your reference table 74 Type of Photons • Identify the type of photons for the transitions form n = 4 to n = 2 in a hydrogen atom E photon = E initial – E final = 4.08 x 10 -19 J f = E / h = 6.15 x 10-14 Hz According to the electromagnetic spectrum, it’s visible light (blue) 75 Atomic Energy Levels & Photon Energy • What are the resources available in the reference table? • How to calculate the energy of photon emitted by an electron changing its energy level? • How to convert eV to Joule? • How to calculate the frequency of an emitted photon? • How to calculate the wavelength of an emitted photon? • How to identify the type of a photon? 76 Steps of Solving Energy Level Problems • Extract the information of Energy Level Diagrams on your reference table • Calculate the energy of photon by E photon = E initial – E final • Convert the photon energy from eV to Joule by 1 eV = 1.60 × 10−19 J • Calculate the photon frequency by f = E photon / h • Calculate the photon wavelength by λ = h c / E photon • Identify the type of a photon according to the electromagnetic spectrum on your reference table 77 Quantum Physics Quantum Physics • Newtonian laws that work so well for the macroworld of our daily life do not apply to events in the microworld of atom • Classic mechanics is for macroworld as quantum mechanics is for the microworld • Measurements in the macroworld is based on certainty while the measurements in the microworld is governed by probability Heisenberg Uncertainty Principle • Using – x = position uncertainty – p = momentum uncertainty • Heisenberg showed that the product Planck’s constant ( x ) ( p ) is always greater than ( h / 4 ) Q&A The End