The Quantum Mechanical Model

Total Page：16

File Type：pdf, Size：1020Kb

The quantum mechanical model Warm up: Sketch the model of the atom throughout history Dalton’s Atomic Model Plum Pudding Model (Thomson) Bohr’s Model Quantum Mechanical Model • 1920’s • Werner Heisenberg (Uncertainty Principle) • Louis de Broglie (electron has wave properes) • Erwin Schrodinger (mathemacal equaons using probability, quantum numbers) Werner Heisenberg: Uncertainty Principle • We can not know both the posiMon and momentum of a parMcle at a given Mme. Balloon in a dark room Louis de Broglie, (France, 1892-1987) Wave ProperMes of Maer (1923) •Since light waves have a parMcle behavior (as shown by Einstein in the Photoelectric Effect), then parMcles could have a wave behavior. •de Broglie wavelength λ= h mv Electron MoMon Around Atom Shown as a de Broglie Wave Erwin Schrodinger, 1925 Quantum (wave) Mechanical Model of the Atom • Derived an equaon that treated the electron as a wave • Was successful in describing the electrons in all atoms – not just the one electron in hydrogen as in the Bohr model Schrodinger’s wave funcMon The quantum mechanical model predicts a three dimensional region around the nucleus, where the electron is likely found, called the atomic orbital Atomic Orbital • Region in space where there is a high probability of finding an electron Atomic Orbital s 2s Degenerate Orbitals • Equal energy orbitals • Oriented differently in space Example of degenerate orbitals: p orbitals hUp://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gif • The d orbitals f orbitals The Electron Cloud • The electron cloud represents posiMons where there is probability of finding an electron. The Electron Cloud The higher the electron density, the higher the probability that an electron may be found in that region. The Electron Cloud for Hydrogen 90% probability of finding the electron within this space Probability Curve for Hydrogen FYI: Schrodinger’s Equaon • ψ is called the wave function and indicates the probability of where an electron may be found. Summary: Quantum Mechanical Model • Electrons are located in specific energy levels. • There is no exact path around the nucleus. • The model esMmates the probability of finding an electron in a certain posiMon. Homework • Create a table comparing and contrasMng the Bohr model with the Quantum Mechanical Model • Read “Tiny Tweezers” on p. 163 for an applicaon of light interacMng with maer Bohr Model Quantum Mechanical Model .

Copy Link

Recommended publications

Wave Nature of Matter: Made Easy (Lesson 3) Matter Behaving As a Wave? Ridiculous!
Wave Nature of Matter: Made Easy (Lesson 3) Matter behaving as a wave? Ridiculous! Compiled by Dr. SuchandraChatterjee Associate Professor Department of Chemistry Surendranath College Remember? I showed you earlier how Einstein (in 1905) showed that the photoelectric effect could be understood if light were thought of as a stream of particles (photons) with energy equal to hν. I got my Nobel prize for that. Louis de Broglie (in 1923) If light can behave both as a wave and a particle, I wonder if a particle can also behave as a wave? Louis de Broglie I’ll try messing around with some of Einstein’s formulae and see what I can come up with. I can imagine a photon of light. If it had a “mass” of mp, then its momentum would be given by p = mpc where c is the speed of light. Now Einstein has a lovely formula that he discovered linking mass with energy (E = mc2) and he also used Planck’s formula E = hf. What if I put them equal to each other? mc2 = hf mc2 = hf So for my photon 2 mp = hfhf/c/c So if p = mpc = hfhf/c/c p = mpc = hf/chf/c Now using the wave equation, c = fλ (f = c/λ) So mpc = hc /λc /λc= h/λ λ = hp So you’re saying that a particle of momentum p has a wavelength equal to Planck’s constant divided by p?! Yes! λ = h/p It will be known as the de Broglie wavelength of the particle Confirmation of de Broglie’s ideas De Broglie didn’t have to wait long for his idea to be shown to be correct.
[Show full text]
Bringing out the Dead Alison Abbott Reviews the Story of How a DNA Forensics Team Cracked a Grisly Puzzle
BOOKS & ARTS COMMENT DADO RUVIC/REUTERS/CORBIS DADO A forensics specialist from the International Commission on Missing Persons examines human remains from a mass grave in Tomašica, Bosnia and Herzegovina. FORENSIC SCIENCE Bringing out the dead Alison Abbott reviews the story of how a DNA forensics team cracked a grisly puzzle. uring nine sweltering days in July Bosnia’s Million Bones tells the story of how locating, storing, pre- 1995, Bosnian Serb soldiers slaugh- innovative DNA forensic science solved the paring and analysing tered about 7,000 Muslim men and grisly conundrum of identifying each bone the million or more Dboys from Srebrenica in Bosnia. They took so that grieving families might find some bones. It was in large them to several different locations and shot closure. part possible because them, or blew them up with hand grenades. This is an important book: it illustrates the during those fate- They then scooped up the bodies with bull- unspeakable horrors of a complex war whose ful days in July 1995, dozers and heavy earth-moving equipment, causes have always been hard for outsiders to aerial reconnais- and dumped them into mass graves. comprehend. The author, a British journalist, sance missions by the Bosnia’s Million It was the single most inhuman massacre has the advantage of on-the-ground knowl- Bones: Solving the United States and the of the Bosnian war, which erupted after the edge of the war and of the International World’s Greatest North Atlantic Treaty break-up of Yugoslavia and lasted from 1992 Commission on Missing Persons (ICMP), an Forensic Puzzle Organization had to 1995, leaving some 100,000 dead.
[Show full text]
Nobel Prize Physicists Meet at Lindau
From 28 June to 2 July 1971 the German island town of Lindau in Nobel Prize Physicists Lake Constance close to the Austrian and Swiss borders was host to a gathering of illustrious men of meet at Lindau science when, for the 21st time, Nobel Laureates held their reunion there. The success of the first Lindau reunion (1951) of Nobel Prize win ners in medicine had inspired the organizers to invite the chemists and W. S. Newman the physicists in turn in subsequent years. After the first three-year cycle the United Kingdom, and an audience the dates of historical events. These it was decided to let students and of more than 500 from 8 countries deviations in the radiocarbon time young scientists also attend the daily filled the elegant Stadttheater. scale are due to changes in incident meetings so they could encounter The programme consisted of a num cosmic radiation (producing the these eminent men on an informal ber of lectures in the mornings, two carbon isotopes) brought about by and personal level. For the Nobel social functions, a platform dis variations in the geomagnetic field. Laureates too the Lindau gatherings cussion, an informal reunion between Thus chemistry may reveal man soon became an agreeable occasion students and Nobel Laureates and, kind’s remote past whereas its long for making or renewing acquain on the last day, the traditional term future could well be shaped by tances with their contemporaries, un steamer excursion on Lake Cons the developments mentioned by trammelled by the formalities of the tance to the island of Mainau belong Mössbauer, viz.
[Show full text]
Otto Stern Annalen 4.11.11
(To be published by Annalen der Physik in December 2011) Otto Stern (1888-1969): The founding father of experimental atomic physics J. Peter Toennies,1 Horst Schmidt-Böcking,2 Bretislav Friedrich,3 Julian C.A. Lower2 1Max-Planck-Institut für Dynamik und Selbstorganisation Bunsenstrasse 10, 37073 Göttingen 2Institut für Kernphysik, Goethe Universität Frankfurt Max-von-Laue-Strasse 1, 60438 Frankfurt 3Fritz-Haber-Institut der Max-Planck-Gesellschaft Faradayweg 4-6, 14195 Berlin Keywords History of Science, Atomic Physics, Quantum Physics, Stern- Gerlach experiment, molecular beams, space quantization, magnetic dipole moments of nucleons, diffraction of matter waves, Nobel Prizes, University of Zurich, University of Frankfurt, University of Rostock, University of Hamburg, Carnegie Institute. We review the work and life of Otto Stern who developed the molecular beam technique and with its aid laid the foundations of experimental atomic physics. Among the key results of his research are: the experimental test of the Maxwell-Boltzmann distribution of molecular velocities (1920), experimental demonstration of space quantization of angular momentum (1922), diffraction of matter waves comprised of atoms and molecules by crystals (1931) and the determination of the magnetic dipole moments of the proton and deuteron (1933). 1 Introduction Short lists of the pioneers of quantum mechanics featured in textbooks and historical accounts alike typically include the names of Max Planck, Albert Einstein, Arnold Sommerfeld, Niels Bohr, Max von Laue, Werner Heisenberg, Erwin Schrödinger, Paul Dirac, Max Born, and Wolfgang Pauli on the theory side, and of Wilhelm Conrad Röntgen, Ernest Rutherford, Arthur Compton, and James Franck on the experimental side. However, the records in the Archive of the Nobel Foundation as well as scientific correspondence, oral-history accounts and scientometric evidence suggest that at least one more name should be added to the list: that of the “experimenting theorist” Otto Stern.
[Show full text]
Heisenberg's Visit to Niels Bohr in 1941 and the Bohr Letters
Klaus Gottstein Max-Planck-Institut für Physik (Werner-Heisenberg-Institut) Föhringer Ring 6 D-80805 Munich, Germany 26 February, 2002 New insights? Heisenberg’s visit to Niels Bohr in 1941 and the Bohr letters1 The documents recently released by the Niels Bohr Archive do not, in an unambiguous way, solve the enigma of what happened during the critical brief discussion between Bohr and Heisenberg in 1941 which so upset Bohr and made Heisenberg so desperate. But they are interesting, they show what Bohr remembered 15 years later. What Heisenberg remembered was already described by him in his memoirs “Der Teil und das Ganze”. The two descriptions are complementary, they are not incompatible. The two famous physicists, as Hans Bethe called it recently, just talked past each other, starting from different assumptions. They did not finish their conversation. Bohr broke it off before Heisenberg had a chance to complete his intended mission. Heisenberg and Bohr had not seen each other since the beginning of the war in 1939. In the meantime, Heisenberg and some other German physicists had been drafted by Army Ordnance to explore the feasibility of a nuclear bomb which, after the discovery of fission and of the chain reaction, could not be ruled out. How real was this theoretical possibility? By 1941 Heisenberg, after two years of intense theoretical and experimental investigations by the drafted group known as the “Uranium Club”, had reached the conclusion that the construction of a nuclear bomb would be feasible in principle, but technically and economically very difficult. He knew in principle how it could be done, by Uranium isotope separation or by Plutonium production in reactors, but both ways would take many years and would be beyond the means of Germany in time of war, and probably also beyond the means of Germany’s adversaries.
[Show full text]
Theory and Experiment in the Quantum-Relativity Revolution
Theory and Experiment in the Quantum-Relativity Revolution expanded version of lecture presented at American Physical Society meeting, 2/14/10 (Abraham Pais History of Physics Prize for 2009) by Stephen G. Brush* Abstract Does new scientific knowledge come from theory (whose predictions are confirmed by experiment) or from experiment (whose results are explained by theory)? Either can happen, depending on whether theory is ahead of experiment or experiment is ahead of theory at a particular time. In the first case, new theoretical hypotheses are made and their predictions are tested by experiments. But even when the predictions are successful, we can’t be sure that some other hypothesis might not have produced the same prediction. In the second case, as in a detective story, there are already enough facts, but several theories have failed to explain them. When a new hypothesis plausibly explains all of the facts, it may be quickly accepted before any further experiments are done. In the quantum-relativity revolution there are examples of both situations. Because of the two-stage development of both relativity (“special,” then “general”) and quantum theory (“old,” then “quantum mechanics”) in the period 1905-1930, we can make a double comparison of acceptance by prediction and by explanation. A curious anti- symmetry is revealed and discussed. _____________ *Distinguished University Professor (Emeritus) of the History of Science, University of Maryland. Home address: 108 Meadowlark Terrace, Glen Mills, PA 19342. Comments welcome. 1 “Science walks forward on two feet, namely theory and experiment. ... Sometimes it is only one foot which is put forward first, sometimes the other, but continuous progress is only made by the use of both – by theorizing and then testing, or by finding new relations in the process of experimenting and then bringing the theoretical foot up and pushing it on beyond, and so on in unending alterations.” Robert A.
[Show full text]
Heisenberg and the Nazi Atomic Bomb Project, 1939-1945: a Study in German Culture
Heisenberg and the Nazi Atomic Bomb Project http://content.cdlib.org/xtf/view?docId=ft838nb56t&chunk.id=0&doc.v... Preferred Citation: Rose, Paul Lawrence. Heisenberg and the Nazi Atomic Bomb Project, 1939-1945: A Study in German Culture. Berkeley: University of California Press, c1998 1998. http://ark.cdlib.org/ark:/13030/ft838nb56t/ Heisenberg and the Nazi Atomic Bomb Project A Study in German Culture Paul Lawrence Rose UNIVERSITY OF CALIFORNIA PRESS Berkeley · Los Angeles · Oxford © 1998 The Regents of the University of California In affectionate memory of Brian Dalton (1924–1996), Scholar, gentleman, leader, friend And in honor of my father's 80th birthday Preferred Citation: Rose, Paul Lawrence. Heisenberg and the Nazi Atomic Bomb Project, 1939-1945: A Study in German Culture. Berkeley: University of California Press, c1998 1998. http://ark.cdlib.org/ark:/13030/ft838nb56t/ In affectionate memory of Brian Dalton (1924–1996), Scholar, gentleman, leader, friend And in honor of my father's 80th birthday ― ix ― ACKNOWLEDGMENTS For hospitality during various phases of work on this book I am grateful to Aryeh Dvoretzky, Director of the Institute of Advanced Studies of the Hebrew University of Jerusalem, whose invitation there allowed me to begin work on the book while on sabbatical leave from James Cook University of North Queensland, Australia, in 1983; and to those colleagues whose good offices made it possible for me to resume research on the subject while a visiting professor at York University and the University of Toronto, Canada, in 1990–92. Grants from the College of the Liberal Arts and the Institute for the Arts and Humanistic Studies of The Pennsylvania State University enabled me to complete the research and writing of the book.
[Show full text]
Wolfgang Pauli 1900 to 1930: His Early Physics in Jungian Perspective
Wolfgang Pauli 1900 to 1930: His Early Physics in Jungian Perspective A Dissertation Submitted to the Faculty of the Graduate School of the University of Minnesota by John Richard Gustafson In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Advisor: Roger H. Stuewer Minneapolis, Minnesota July 2004 i © John Richard Gustafson 2004 ii To my father and mother Rudy and Aune Gustafson iii Abstract Wolfgang Pauli's philosophy and physics were intertwined. His philosophy was a variety of Platonism, in which Pauli’s affiliation with Carl Jung formed an integral part, but Pauli’s philosophical explorations in physics appeared before he met Jung. Jung validated Pauli’s psycho-philosophical perspective. Thus, the roots of Pauli’s physics and philosophy are important in the history of modern physics. In his early physics, Pauli attempted to ground his theoretical physics in positivism. He then began instead to trust his intuitive visualizations of entities that formed an underlying reality to the sensible physical world. These visualizations included holistic kernels of mathematical-physical entities that later became for him synonymous with Jung’s mandalas. I have connected Pauli’s visualization patterns in physics during the period 1900 to 1930 to the psychological philosophy of Jung and displayed some examples of Pauli’s creativity in the development of quantum mechanics. By looking at Pauli's early physics and philosophy, we gain insight into Pauli’s contributions to quantum mechanics. His exclusion principle, his influence on Werner Heisenberg in the formulation of matrix mechanics, his emphasis on firm logical and empirical foundations, his creativity in formulating electron spinors, his neutrino hypothesis, and his dialogues with other quantum physicists, all point to Pauli being the dominant genius in the development of quantum theory.
[Show full text]
Some Famous Physicists Ing Weyl’S Book Space, Time, Matter, the Same Book That Heisenberg Had Read As a Young Man
Heisenberg’s first graduate student was Felix Bloch. One day, while walking together, they started to discuss the concepts of space and time. Bloch had just finished read- Some Famous Physicists ing Weyl’s book Space, Time, Matter, the same book that Heisenberg had read as a young man. Still very much Anton Z. Capri† under the influence of this scholarly work, Bloch declared that he now understood that space was simply the field of Sometimes we are influenced by teachers in ways that, affine transformations. Heisenberg paused, looked at him, although negative, lead to positive results. This happened and replied, “Nonsense, space is blue and birds fly through to Werner Heisenberg1 and Max Born,2 both of whom it.” started out to be mathematicians, but switched to physics There is another version of why Heisenberg switched to due to encounters with professors. physics. At an age of 19, Heisenberg went to the University As a young student at the University of Munich, Heisen- of Göttingen to hear lectures by Niels Bohr.4 These lec- berg wanted to attend the seminar of Professor F. von tures were attended by physicists and their students from Lindemann,3 famous for solving the ancient problem of various universities and were jokingly referred to as “the squaring the circle. Heisenberg had Bohr festival season.” Here, Bohr expounded on his latest read Weyl’s book Space, Time, Matter theories of atomic structure. The young Heisenberg in the and, both excited and disturbed by the audience did not hesitate to ask questions when Bohr’s abstract mathematical arguments, had explanations were less than clear.
[Show full text]
Quantum Mechanics and Atomic Physics Lecture 2: Rutherfordrutherford--Bohrbohr Atom and Dbdebrog Lie Matteratter--Waves Prof
Quantum Mechanics and Atomic Physics Lecture 2: RutherfordRutherford--BohrBohr Atom and dBdeBrog lie Matteratter--Waves http://www.physics.rutgers.edu/ugrad/361 Prof. Sean Oh HW schedule changed!! First homework due on Wednesday Sept 14 and the second HW will be due on Monday Sept 19! HW1 Will be posted today Review from last time Planck’s blackbody radiation formula Explained phenomena such as blackbody radiation and the photoelectric effect. Light regarded as stream of particles, photons because m=0 Also, E=hfE=hf(f: frequency), so pc=hfpc=hf Î p=hf/c= h/λ, because λ=c/f (λ: wave length, c: speed of light) Composition of Atoms If matter is primarily composed of atoms, what are atoms composed of? J.J. Thomson (1897): Identification of cathode rays as electrons and measurement of ratio (e/m) of these particles Electron is a constituent of all matter! Humankind’s first glimpse into subatomic world! Robert Millikan (1909): Precise measurement of electric charge Showed that particles ~1000 times less massive than the hydrogen atom exist Ru the rfo rd, w ith Ge ige r & Ma rs de n (1910): Es ta blis he d the nuclear model of the atom Atom = compact positively charged nucleus surrounded by an orbiting electron clo ud Thomson Model of Atoms (1898) Uniform, massive positive charge Much less massive point electrons embedded inside. Radius R. Rutherford’s α --scatteringscattering apparatus Ernest Rutherford, with Hans Geiger and Ernest Marsden scattered alpha particles from a radioactive source off of a thin gold foil. (1911) http://hyperphysics.phy-astr.gsu.edu/Hbase/hframe.html Alpha deflection off of an electron --44 o Experiment was set up to see if any θ~me/mα ~ 10 rad < 0.01 alpha particles can be scattered But what about deflection off a through a l a rge an g le.
[Show full text]
Otto Stern Annalen 22.9.11
September 22, 2011 Otto Stern (1888-1969): The founding father of experimental atomic physics J. Peter Toennies,1 Horst Schmidt-Böcking,2 Bretislav Friedrich,3 Julian C.A. Lower2 1Max-Planck-Institut für Dynamik und Selbstorganisation Bunsenstrasse 10, 37073 Göttingen 2Institut für Kernphysik, Goethe Universität Frankfurt Max-von-Laue-Strasse 1, 60438 Frankfurt 3Fritz-Haber-Institut der Max-Planck-Gesellschaft Faradayweg 4-6, 14195 Berlin Keywords History of Science, Atomic Physics, Quantum Physics, Stern- Gerlach experiment, molecular beams, space quantization, magnetic dipole moments of nucleons, diffraction of matter waves, Nobel Prizes, University of Zurich, University of Frankfurt, University of Rostock, University of Hamburg, Carnegie Institute. We review the work and life of Otto Stern who developed the molecular beam technique and with its aid laid the foundations of experimental atomic physics. Among the key results of his research are: the experimental determination of the Maxwell-Boltzmann distribution of molecular velocities (1920), experimental demonstration of space quantization of angular momentum (1922), diffraction of matter waves comprised of atoms and molecules by crystals (1931) and the determination of the magnetic dipole moments of the proton and deuteron (1933). 1 Introduction Short lists of the pioneers of quantum mechanics featured in textbooks and historical accounts alike typically include the names of Max Planck, Albert Einstein, Arnold Sommerfeld, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Paul Dirac, Max Born, and Wolfgang Pauli on the theory side, and of Konrad Röntgen, Ernest Rutherford, Max von Laue, Arthur Compton, and James Franck on the experimental side. However, the records in the Archive of the Nobel Foundation as well as scientific correspondence, oral-history accounts and scientometric evidence suggest that at least one more name should be added to the list: that of the “experimenting theorist” Otto Stern.
[Show full text]
Presentation Slides
How Did We Find Out About Quantum Mechanics? Dan Styer Department of Physics and Astronomy Oberlin College Max Planck (age 42 in 1900) Albert Einstein (age 26 in 1905) Einstein’s four 1905 papers: Quantum mechanics of light (heuristic photoelectric effect) Brownian motion (atoms exist!) On the Electrodynamics of Moving Bodies Does the Inertia of a Body Depend on its Energy Content? (E = mc2) Einstein’s four 1905 papers: Quantum mechanics of light (heuristic photoelectric effect) “is very revolutionary” Brownian motion (atoms exist!) On the Electrodynamics of Moving Bodies “a modification of the theory of space and time” Does the Inertia of a Body Depend on its Energy Content? (E = mc2) Niels Bohr (age 28 in 1913) Werner Heisenberg (age 24 in 1925) Werner Heisenberg (age 24 in 1925) Helgoland Göttingen Wolfgang Pauli (age 25 in 1925) Louise de Broglie (age 31 in 1923) Louise de Broglie Erwin Schrödinger (age 38 in 1925) Arosa, Switzerland Arosa, Switzerland Arosa, Switzerland Erwin Schrödinger (age 38 in 1925) Erwin Schrödinger Crater Schrödinger Matrix Mechanics (Heisenberg, Born) versus Wave Mechanics (Schrödinger) Matrix and Wave Mechanics proven equivalent in 1926 by Schrödinger, Pauli, and Carl Eckert (age 24) Carl Eckert (photo 1948) Paul A. M. Dirac (age 24 in 1926) Paul A. M. Dirac Satyendra Bose 1924-25: quantum mechanics applied to large number of particles (with A. Einstein) (age 31 in 1925) Satyendra Bose 1925: predicted a new phase of matter – solid, liquid, gas, and “Bose condensate” Michael Fisher 1970s: extended this work Experimental verification! 1995 Experimental verification! 1995 by Carl Wieman and Eric Cornell Experimental verification! extended to “fermionic condensate” by Deborah Jin in 2003 Linus Pauling (age 30 in 1931) Linus Pauling and family Linus Pauling Linus Pauling gave his name to Linus Torvalds who gave his name to Linux Maria Goeppert Mayer nuclear shell theory, 1950 Crater Goeppert Mayer on Venus Maria Goeppert Mayer 1950: nuclear shell theory 1960: appointed professor at U.
[Show full text]