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FI 3103 Quantum Physics the Emergence of Quantum Physics

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FI 3103 Quantum Physics the Emergence of Quantum Physics 05/09/2014 FI 3103 Quantum Physics Alexander A. Iskandar Physics of Magnetism and Photonics Research Group Institut Teknologi Bandung The Emergence of Quantum Physics Wave Properties of Particle Bohr Atom Alexander A. Iskandar Emergence of Quantum Physics 2 1 05/09/2014 Wave Properties of Particle . Louis-Victor-Pierre-Raymond, 7th duc de Broglie (15 August 1892 – 19 March 1987) was a French physicist who made ground breaking contributions to quantum theory. In his 1924 PhD thesis (thesis advisor : Paul Langevin), he postulated the wave nature of electrons and suggested that all matter has de Broglie wave properties. This concept is known as wave-particle duality or the de Broglie hypothesis. h h h h de Broglie p c p mv wavelength photon momentum Alexander A. Iskandar Emergence of Quantum Physics 3 Proof of Wave Properties of Particle Electron Diffraction . J. J. Thomson was awarded the Physics Prize in 1906 for showing that electrons are particles. His son, George Paget Thomson, received the same prize in 1937 (together with Davisson) for showing that they also have the properties of waves. J.J. Thomson C.J. Davisson – L. Germer C.J. Davisson G.P. Thomson Alexander A. Iskandar Emergence of Quantum Physics 4 2 05/09/2014 Bragg’s X-ray Diffraction . Nobel Prize in Physics 1915. William Lawrence Bragg, was to date the youngest Nobel Laureate (he was 25 years old when he received the Nobel Prize). W.H. Bragg W.L. Bragg Alexander A. Iskandar Emergence of Quantum Physics 5 Davisson-Germer Experiment de Broglie relationship p mv 2mE 2meV C.J. Davisson – L. Germer Alexander A. Iskandar Emergence of Quantum Physics 6 3 05/09/2014 Electron Diffraction-Interference . What happens if we send electrons through a double slit apparatus? • initially, the pattern looks random • start to see interference • characteristic interference pattern Alexander A. Iskandar Emergence of Quantum Physics 7 Electron Diffraction-Interference Alexander A. Iskandar Emergence of Quantum Physics 8 4 05/09/2014 Electron Diffraction-Interference Alexander A. Iskandar Emergence of Quantum Physics 9 Louis de Broglie (15 August 1892 – 19 March 1987) . For his wave properties of particle, de Broglie won the Nobel Prize for Physics in 1929 for the proposal that he put forward in 1924 and proven by experiment in 1927. The wave-like behaviour of particles discovered by de Broglie was used by Erwin Schrödinger in his formulation of wave de Broglie mechanics. Alexander A. Iskandar Emergence of Quantum Physics 10 5 05/09/2014 Limit of Wave Properties of Particle . Example 1.6 . At macroscopic scale, we will not be able to see the wave nature of particles. A 0.1 mm diameter water droplet moving at 1 mm/s will have a de Broglie wavelength of 10-25 m, which is tens of order of magnitude smaller than the size of a proton. The smallness of Planck’s constant that makes the separation of wave and particle properties so striking in the classical domain. Alexander A. Iskandar Emergence of Quantum Physics 11 Evolution of the Atomic Model . Dalton atomic model (1803) • Elements are made of extremely small particles called atoms. • Atoms of different elements differ in size, mass, and other properties • The law of multiple proportions . Thomson atomic model (plum- pudding model, 1904) • The atom as being made up of negatively charged corpuscles orbiting in a sea of positive charge. Rutherford atomic model (1911) • Atoms have their charge concentrated in a very small nucleus, and electrons are tiny particles orbiting the nucleus. Bohr atomic model (1913) Alexander A. Iskandar Emergence of Quantum Physics 12 6 05/09/2014 Thomson Cathode Ray Experiment . In 1897, Thomson showed that cathode rays were composed of a previously unknown negatively charged particle, and thus is credited with the discovery and identification of the electron. J. J. Thomson was awarded the Physics Prize in 1906 for showing that electrons are particles. Alexander A. Iskandar Emergence of Quantum Physics 13 Thomson Cathode Ray Experiment . J. J. Thomson also performed further experiments using magnetic field to determine the ratio of e/m. Alexander A. Iskandar Emergence of Quantum Physics 14 7 05/09/2014 Thomson Cathode Ray Experiment . Thomson’s method of measuring the ratio of the electron’s charge to mass was to send electrons through a region containing a magnetic field perpendicular to an electric field. Alexander A. Iskandar Emergence of Quantum Physics 15 Thomson Cathode Ray Experiment . An electron moving through the electric field is accelerated by a force: Fyy ma eE . Electron angle of deflection: v at eE yy t tan( ) 2 vx v00m v v0 . Then turn on the magnetic field, which deflects the electron against the electric field force. F eE ev00 B . The magnetic field is then adjusted until the net force is zero. eE tan( ) EB v0 v/0 EB 2 m(/) E B eEtan( ) . Charge to mass ratio : mB2 Alexander A. Iskandar Emergence of Quantum Physics 16 8 05/09/2014 Thomson’s Plum-Pudding model . Thomson imagined the atom as being made up of these corpuscles orbiting in a sea of positive charge; this was his plum pudding model. This model was later proved incorrect when Ernest Rutherford showed that the positive charge is concentrated in the nucleus of the atom. J.J. Thomson Alexander A. Iskandar Emergence of Quantum Physics 17 Geiger-Marsden Experiment . In 1909, Rutherford inspired Hans Geiger and Ernest Marsden to perform the gold-foil experiment. Geiger Marsden Alexander A. Iskandar Emergence of Quantum Physics 18 9 05/09/2014 Geiger-Marsden Experiment 1 N sin 4 2 PhET: Rutherford Scattering Alexander A. Iskandar Emergence of Quantum Physics 19 Rutherford Atomic Model . In 1911, Rutherford put forward the theory that atoms have their charge concentrated in a very small nucleus, and electrons are tiny particles orbiting the nucleus. Geiger Marsden Rutherford model of the atom. Alexander A. Iskandar Emergence of Quantum Physics 20 10 05/09/2014 Ernst Rutherford (30 August 1871 – 19 October 1937) . Awarded the Nobel Prize in Chemistry in 1908 for his investigations into the disintegration of the elements, and the chemistry of radioactive substances, work that was done at McGill Univ., Canada. Rutherford was born in New Zealand, where he studied at Canterbury College, University of New Zealand. 1895 Rutherford was awarded a scholarship to travel to England for postgraduate study at the Cavendish Laboratory, University of Cambridge. He was among the first of the 'aliens' (those without a Cambridge degree) allowed to do research at the university, under the inspiring leadership of J. J. Thomson. Alexander A. Iskandar Emergence of Quantum Physics 21 Ernst Rutherford (30 August 1871 – 19 October 1937) . In 1898 Thomson offered Rutherford the chance of a post at McGill University in Montreal, Canada. In 1907 he moved to Victoria University of Manchester (today University of Manchester) in the UK. He is widely credited with first "splitting the atom" in 1917 in a nuclear reaction between nitrogen and alpha particles, in which he also discovered (and named) the proton. Alexander A. Iskandar Emergence of Quantum Physics 22 11 05/09/2014 Problem with Rutherford atomic model . From classical EM theory, an accelerated electric charge radiates energy (electromagnetic radiation), which means total energy must decrease. And the radius r must decrease and the electron must fall to the nucleus! Alexander A. Iskandar Emergence of Quantum Physics 23 Line Spectra . Chemical elements were observed to produce unique wavelengths of light when burned or excited in an electrical discharge. Alexander A. Iskandar Emergence of Quantum Physics 24 12 05/09/2014 Balmer Series . In 1885, Johann Balmer found an empirical formula for the wavelength of the visible hydrogen line spectra in nm: nm (where k = 3,4,5…) Johann Balmer Alexander A. Iskandar Emergence of Quantum Physics 25 Rydberg Formula . As more scientists discovered emission lines at infrared and ultraviolet wavelengths, the Balmer series equation was extended to the Rydberg equation (1888): J. Rydberg Alexander A. Iskandar Emergence of Quantum Physics 26 13 05/09/2014 Bohr’s Postulate . In 1913, Bohr put forward 3 postulates that govern the atomic structure which can explained the spectral lines and bypass the stability problem. These postulates are • An atomic system can only exist in a discrete set of stationary states, with discrete values of energy, and any change of the energy of the system, including emission and absorption of electromagnetic radiation must take place by a complete transition between two stationary states. • The radiation absorbed or emitted during a transition between two stationary states of energies E1 and E2 (E1 > E2) is characterized by a unique frequency given by E1 E2 h Alexander A. Iskandar Emergence of Quantum Physics 27 Bohr’s Postulate Alexander A. Iskandar Emergence of Quantum Physics 28 14 05/09/2014 Bohr’s Postulate • The stationary states corresponds to a set of allowed orbits in the Rutherford atomic model. They are determined by the requirement that the kinetic energy of the electron in the orbit is related to the frequency f of the motion of the electron in that orbit by 1 m v2 1 nhf 2 e 2 where n = 1, 2, 3, … For circular orbits this reduces to the statement that the angular momentum takes on integer values in units of h/2p, so that h v Lcircular mevr n n f 2p 2pr Alexander A. Iskandar Emergence of Quantum Physics 29 Bohr’s Postulate . Alternatively, for a circular orbit, we can consider that the electron is a standing wave in an orbit around the proton. This standing wave will have nodes and be an integral number of wavelengths. h 2pr n n p .
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