NJIT Physics 320: Astronomy and Astrophysics – Lecture V Carsten Denker Physics Department Center for Solar–Terrestrial Research

October 1st, 2003NJIT Center for Solar-Terrestrial Research The Interaction of Light and Matter  Spectral Lines  Photons  The Bohr Model of the Atom  Quantum Mechanics and Wave–Particle Duality

October 1st, 2003NJIT Center for Solar-Terrestrial Research Electromagnetic Spectrum

October 1st, 2003NJIT Center for Solar-Terrestrial Research 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

October 1st, 2003NJIT Center for Solar-Terrestrial Research 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.

October 1st, 2003NJIT Center for Solar-Terrestrial Research Spectroscopy  Prisms  Diffraction gratings  Transmission grating  Reflection grating Resolving power

October 1st, 2003NJIT Center for Solar-Terrestrial Research Photoelectric Effect

October 1st, 2003NJIT Center for Solar-Terrestrial Research Compton Effect In a collision between a photon and an electron initially at rest, both the (relativistic) momentum and energy are conserved. Compton wavelength

October 1st, 2003NJIT Center for Solar-Terrestrial Research 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: m p = 1836  m e

October 1st, 2003NJIT Center for Solar-Terrestrial Research Group Assignment Problem 5.7  Verify that the units of Planck’s constant are the units of angular momentum!

October 1st, 2003NJIT Center for Solar-Terrestrial Research Hydrogen Atom m = 1UV [122, 103, 97, …] nmLyman m = 2Visible [656, 486, 434, …] nmBalmer m = 3IR [1875, 1282, 1094, …] nmPaschen m = 4IR [4051, 2625, 2165, …] nmBrackett m = 5IR [7458, 4652, …] nmPfundt Planetary model of the hydrogen atom?

October 1st, 2003NJIT Center for Solar-Terrestrial Research 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 E photon = E high – E low results in the emission of an energy quantum, i. e., a photon.

October 1st, 2003NJIT Center for Solar-Terrestrial Research Bohr Atom Coloumb’s law Reduced mass Total mass

October 1st, 2003NJIT Center for Solar-Terrestrial Research Quantization of angular momentum

October 1st, 2003NJIT Center for Solar-Terrestrial Research Bohr Atom (cont.)

October 1st, 2003NJIT Center for Solar-Terrestrial Research 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.

October 1st, 2003NJIT Center for Solar-Terrestrial Research 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.

October 1st, 2003NJIT Center for Solar-Terrestrial Research Quantum Mechanics and Wave–Particle Duality De Broglie frequency De Broglie wavelength Heisenberg’s uncertainty principle

October 1st, 2003NJIT Center for Solar-Terrestrial Research Problem 4.5

October 1st, 2003NJIT Center for Solar-Terrestrial Research Problem 4.13

October 1st, 2003NJIT Center for Solar-Terrestrial Research Problem 4.18

October 1st, 2003NJIT Center for Solar-Terrestrial Research 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 8 th, 2003 at the beginning of the lecture!  Exhibition name competition!

October 1st, 2003NJIT Center for Solar-Terrestrial Research Homework  Homework is due Wednesday October 8 th, 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!