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Physics 320: Astronomy and Astrophysics – Lecture V Carsten Denker Physics Department Center for Solar–Terrestrial Research NJIT The Interaction of Light and Matter Spectral Lines Photons The Bohr Model of the Atom Quantum Mechanics and Wave–Particle Duality NJIT Center for Solar-Terrestrial Research October 1st, 2003 Electromagnetic Spectrum NJIT Center for Solar-Terrestrial Research October 1st, 2003 Spectral Lines Auguste Comte 1835 in Positive Philosophy: We see how we may determine their forms their distances, their bulk, their motions, but we can never know anything of their chemical or minerological structure. William Wollaston, Joseph Fraunhofer, Robert Bunsen, Gustav Kirchhoff, … spectroscopy NJIT Center for Solar-Terrestrial Research October 1st, 2003 Kirchhoff’s Laws A hot (< 0 K), dense gas or solid object produces produces a continuous spectrum with no dark spectral lines. A hot, diffuse gas produces bright spectral lines (emission lines). A cool, diffuse gas in front of a source of a continuous spectrum produces dark spectral lines (absorption lines) in the continuous spectrum. NJIT Center for Solar-Terrestrial Research October 1st, 2003 Spectroscopy Prisms Diffraction gratings Transmission grating Reflection grating d sin n and n 1, 2, 3, ... nN nN Resolving power NJIT Center for Solar-Terrestrial Research October 1st, 2003 Photoelectric Effect Ephoton h hc K max Ephoton h NJIT Center for Solar-Terrestrial Research hc October 1st, 2003 Compton Effect Ephoton h hc f i pc h 1 cos me c Compton wavelength c h 0.0243 Å me c In a collision between a photon and an electron initially at rest, both the (relativistic) momentum and energy are conserved. NJIT Center for Solar-Terrestrial Research October 1st, 2003 The Bohr Model of the Atom Wave–particle duality of light Rutherford 1911 Au: It was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you fired a 15–inch shell at a piece of tissue paper and it came back an hit you. discovery of a minute, massive, positively charged atomic nucleus Proton: mp = 1836 me NJIT Center for Solar-Terrestrial Research October 1st, 2003 Group Assignment Problem 5.7 Verify that the units of Planck’s constant are the units of angular momentum! m m2 L mvr kg m = kg s s E J m m2 E h h -1 = Js = Nm s = kg 2 m s = kg s s s NJIT Center for Solar-Terrestrial Research October 1st, 2003 Hydrogen Atom 1 1 RH 2 and RH 109677.585 0.008 cm 1 4 n 1 1 1 RH 2 2 and m n m n 1 Planetary model of the hydrogen atom? m=1 UV [122, 103, 97, …] nm Lyman m=2 Visible [656, 486, 434, …] nm Balmer m=3 IR [1875, 1282, 1094, …] nm Paschen m=4 IR [4051, 2625, 2165, …] nm Brackett m=5 IR [7458, 4652, …] nm Pfundt NJIT Center for Solar-Terrestrial Research October 1st, 2003 Bohr’s Postulates Only orbits are stable, where the angular momentum of the electron is quantized L = nh/2=nħ, and will not radiate in spite of the electron’s acceleration. Every allowed orbit corresponds to a distinct energy level and the transition from a distant orbit to an orbit closer to the nucleus Ephoton = Ehigh – Elow results in the emission of an energy quantum, i. e., a photon. NJIT Center for Solar-Terrestrial Research October 1st, 2003 Bohr Atom q1q2 FE r 3 4 0 r 1 Coloumb’s law me m p (me )(1836me ) 0.9994556me me m p me 1836me M me m p me 1836me 1837me M m p and Reduced mass Total mass me 1 q1q2 v2 1 e2 v2 F a r 2 r 3 2 4 0 r r 4 0 r r NJIT Center for Solar-Terrestrial Research October 1st, 2003 1 2 1 e2 1 e2 K v and U 2 K 2 8 0 r 4 0 r 1 e2 E K U K 2K K 8 0 r L vr n and h = 2 Quantization of angular momentum 1 e 1 2 1 vr 1 n K v 2 8 0 r 2 2 r 2 r 2 2 rn 4 0 2 e2 2 2 n2 a0 n2 and a0 5.29 1011 m 0.529 Å NJIT Center for Solar-Terrestrial Research October 1st, 2003 Bohr Atom (cont.) 1 e2 e4 1 1 En 2 2 13.6 eV 2 8 0 rn 2 n n E1 13.6 eV r1 a0 0.529 Å E2 E1 / 4 3.40 eV r2 4a0 2.12 Å Ephoton Ehigh Elow e4 1 e4 1 2 2 2 2 2 nhigh 2 nlow hc e4 1 1 2 3 2 4 c nhigh nlow 1 EH 1 1 RH 2 2 nhigh nlow e4 and RH 3 4 c hc 1 1 (13.6 eV) 2 2 1.89 eV 6565 Å EH 3 2 NJIT Center for Solar-Terrestrial Research October 1st, 2003 Kirchhoff’s Laws Revisited A hot, dense gas or hot solid object produces a continuous spectrum with no dark spectral lines. This is the continuous spectrum of black body radiation, described by the Planck functions B(T) and B(T), emitted at any temperature above absolute zero. The wavelength max at which the Planck function B(T) obtains its maximum is given by Wien’s displacement law. NJIT Center for Solar-Terrestrial Research October 1st, 2003 Kirchhoff’s Laws Revisited (cont.) A hot, diffuse gas produces bright emission lines. Emission lines are produced when an electron makes a downward transition from a higher to a lower orbit. The energy lost by the electron is carried away by the photon. A cool, diffuse gas in front of a source of continuous spectrum produces dark absorption lines in the continuous spectrum. Absorption lines are produced when an electron makes a transition from a lower to a higher orbit. If the incident photon in the continuous spectrum has exactly the right amount of energy, equal to the difference in energy between a higher orbit and the electron’s initial orbit, the photon is absorbed by the atom and the electron makes an upward transition to the higher orbit. NJIT Center for Solar-Terrestrial Research October 1st, 2003 Quantum Mechanics and Wave–Particle Duality E h De Broglie frequency h p De Broglie wavelength 1 2 1 E t 2 xp xp or E t NJIT Center for Solar-Terrestrial Research Heisenberg’s uncertainty principle October 1st, 2003 Problem 4.5 (a) (b) (c ) u 1 u2 0.8 1 2 0.6 and Lmoving 60 m c c t P Lmoving / 0.8c 0.25 μs 60 m Lrest Lmoving 100 m 0.6 1 Lmoving Lrest 0.6 60 m 36 m (d ) tT 100 m/0.8c 0.417 μs (e) Lrest Lmoving 100 m 36 m 64 m tT 64 m / 0.8c 0.267 μs NJIT Center for Solar-Terrestrial Research October 1st, 2003 Problem 4.13 v A u 0.8c and vB 0.6c (Frame of reference @ rest = Earth) vB u vB 1 uvB / c 2 (Eqn. 4.40) 0.6c 0.8c 0.946c 2 1 (0.8c)( 0.6c) / c vA 0.946c = NJIT Center for Solar-Terrestrial Research October 1st, 2003 Problem 4.18 E mc 2 (Eqn. 4.46) E 2 ( mc 2 ) 2 E m c mc 2 2 4 2 2 mc 2 2 mc 2 mc 2 mc 2 mc 2 (Eqn. 4.48) p 2 c 2 mc 2 (1 )mc 2 (1 ) Kmc 2 (1 ) p2 p2 K K if v m(1 ) 2m NJIT Center for Solar-Terrestrial Research c October 1st, 2003 Homework Class Project Prepare a 200 – 250 word abstract for one of the five topics mentioned in the storyline Important scientific facts Form of presentation Learning goals Homework is due Wednesday October 8th, 2003 at the beginning of the lecture! Exhibition name competition! NJIT Center for Solar-Terrestrial Research October 1st, 2003 Homework is due Wednesday October 8th, 2003 at the beginning of the lecture! Homework assignment: Problems 5.4, 5.5, and 5.15 Late homework receives only half the credit! The homework is group homework! Homework should be handed in as a text document! Homework NJIT Center for Solar-Terrestrial Research October 1st, 2003