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Atoms and Spectra Atoms and Spectra Relativity and Astrophysics Lecture 11 Terry Herter Outline Bohr Model of the Atom Electronic Transitions Hydrogen Atom Other elements – Spectral signatures 21-cm Hydrogen line A2290-11 A2290-11 Monday: Tuesday: 02:00 – 04:00 pm 11:00 – 12:00 am If you can’t make these, set up an appointment. Prelim Wednesday, Sept. 23 Closed book and notes, will cover material through last Friday Should know My office hours are: Spacetime interval, fundamental postulates of Special Relativity, simultaneity and other issues raise by relativity Will have both qualitative and quantitative questions Lorentz Transformation equations will be provided (if needed) You may want to bring a calculator Atoms and Spectra 2 1 Atoms and Spectra Where does light come from? It had been known during the 19th century that If we picture an electron as in orbit around the nucleus, it should radiate light Changing direction is acceleration! But if the electron radiated, it would lose energy and soon spiral into the nucleus. The world would collapse instantly! Accelerated charges produce light, and hence emit energy Fortunately it doesn’t. What is wrong with this picture? Enter Quantum Mechanics (QM) Quantum Mechanics was developed during the revolution which occurred in physics from 1900 - 1930. Both Special Relativity and General Relativity were developed during this time. A2290-11 Atoms and Spectra 3 The Bohr Model of the Atom e Niels Bohr 1913: Formulated 3 rules regarding atoms. 1. Electrons can only be in discrete orbits. 2. A photon can be emitted or absorbed by an atom only when an electron jumps from one orbit to another. 3. The photon energy (E) equals the energy difference between the orbits. E = hf = hc/ since c = f, and f = c/. A2290-11 A2290-11 Atoms and Spectra 4 2 Atoms and Spectra Quantum Numbers (Q.N.) An electron can reside in one of many orbits. n = number of orbit = Principal Q.N. n = 1 is the lowest energy state. If n > 1, then the atom is “excited.” A2290-11 Electronic “Orbits” in an Atom n= 3 2 1 Atoms and Spectra Atomic Energy Levels 5 Energy Level Diagram 4 3 2 Emission Absorption Energy n=1 4 3 2 1 A schematic representation of the orbital energy levels. A2290-11 A2290-11 Atoms and Spectra 6 3 Atoms and Spectra Electronic Transitions An electron transition occurs when a electron moves between to orbits. When absorption of a photon occurs, an electron goes up, e.g. from n=1 to n=2. Emission of a photon occurs when an electron moves down, e.g. from n=2 to n=1. A2290-11 Atoms and Spectra 7 Spectra from Atoms A spectrum is the intensity of light seen from an object at different wavelengths. e.g. done by spectroscopy with a prism. Individual atoms, like H, show spectral lines, i.e. For H, these are the Balmer lines in the visible. For a “Conversational” lecture on spectral lines see http://www.colorado.edu/physics/2000/quantumzone/ A2290-11 A2290-11 Atoms and Spectra 8 4 Atoms and Spectra The Spectrum of Hydrogen H has one electron => simplest spectrum. Discrete emission and absorption lines Need a photon of the correct energy to move up a level. Spectral lines occur in ultraviolet, visible, infrared, and radio. Visible lines called Balmer lines. H H H H ... 4000 5000 (A) 6000 7000 Note the discrete “lines” where there is emission. A2290-11 Atoms and Spectra 9 Hydrogen Energy Level Diagram 4 3 12.75 eV 12.09 eV H H 2 H 10.20 eV For instance, the energy difference between n = 2 and n = 1 in H is 10.2 eV. Balmer Lines Ly Ly The energies in atoms are usually expressed in electron volts (eV). 1 eV = 1.6 x 10-19 J Ly Since E = hc/ Lyman Lines n=1 0 eV Ground State = Lowest Energy Level Lyman Lines - Ultraviolet A2290-11 A2290-11 Ly: Ly: Ly: … Balmer Lines - Visible n=2 1, = 1216 A n=3 1, = 1026 A n=4 1, = 973 A H: H: H: … Atoms and Spectra n=3 2, = 6563 A n=4 2, = 4861 A n=5 2, = 4341 A 10 5 Atoms and Spectra Hydrogen Balmer Spectrum: Revisited 4 3 12.75 eV 12.09 eV H H 2 H Balmer Lines - Visible 10.20 eV Balmer Lines n=1 0 eV H H n=3 2, = 6563 A n=4 2, = 4861 A n=5 2, = 4341 A H: H: H: … Notes: (1) The energy levels get closer together as the quantum numbers get larger. (2) The greater the difference between the quantum numbers, the larger the energy of the photon emitted or absorbed. H H ... 4000 A2290-11 6000 5000 (A) 7000 Atoms and Spectra 11 The “Continuum” Continuum for free electrons 4 3 The ionization energy of hydrogen is 13.6 eV. To ionize an electron from the ground state (n=1) of hydrogen requires photons of energy 13.6 eV or greater. => < 912 A 2 If h > 13.6 eV, electron can leave the atom. 13.6 eV The energy of an electron in the continuum is not quantized (it’s continuous). n=1 Ground State = Lowest Energy Level An electron in the continuum has escaped from the proton. A2290-11 A2290-11 This can happen if the Hydrogen atom absorbs a photon with energy (h) greater than 13.6 eV. And the hydrogen atom is “ionized.” Atoms and Spectra 12 6 Atoms and Spectra Ionization and Ions Neutral HeI Once Ionized HeII Twice Ionized HeIII If a photon has enough energy, it can ionize an atom, i.e. promote an electron into the continuum. An atom becomes an ion when one or more electrons have been removed. Adding an extra electron also creates an ion but this is much more difficult and rare. A2290-11 Atoms and Spectra 13 Notation Astronomers use the following notation to indicate the ionic state of an atom. Suffix I II III etc. A2290-11 Example HeI, OI HeII, OII HeIII, OIII Notes (on ionization): A2290-11 Meaning neutral once ionized twice ionized It takes progressively more energy to remove successive electrons from an atom. That is, it is much harder to ionize HeII than HeI. Note: You can not have HeIV ! Atoms and Spectra 14 7 Atoms and Spectra Spectra of several elements White Light Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen A2290-11 Atoms and Spectra 15 Spectra of several elements White Light Hydrogen Sodium Solid materials have a continuous spectrum rather than a discrete one (somewhat like white light). This is different from individual atoms. Examples: A2290-11 A2290-11 Tungsten filament light bulb - continuous Fluorescent lamp - discrete Atoms and Spectra 16 8 Atoms and Spectra Spectral Signatures: Astronomy’s Rosetta Stone Spectral signature: Each ion has a unique set of spectral lines associated with it. This is of fundamental importance to astronomy, allowing the identification of elements clear across the galaxy and universe. With spectral signatures we can identify oxygen, carbon, iron, etc. In addition these signature provides information on: Chemical composition of the stars Abundances of the elements Physical conditions of the gases Densities and Temperatures A2290-11 Atoms and Spectra 17 Hydrogen 21-cm Radiation A2290-11 A2290-11 An important spectral line in astronomy for measuring the gas between stars is the 21-cm line of Hydrogen. This is in the radio part of the spectrum. The n = 1 level (ground state) of H is actually “split” into 2 levels separated by a very small energy. This splitting is due to the fact that the electron and proton have intrinsic spin, i.e. they behave like small magnets. When the North poles are aligned the energy is higher than when they are not. Atoms and Spectra 18 9 Atoms and Spectra 21-cm Radiation (cont’d) Poles Aligned (higher energy state) N Poles Opposite (lower energy state) N N S S S N S A 21-cm photon is emitted when poles go from being aligned to opposite (a spin flip). A2290-11 Atoms and Spectra 19 Hydrogen Energy Level Diagram – 21 cm line 4 3 12.75 eV 12.09 eV H 2 H H Balmer Lines Ly Ly Ly 10.20 eV Not to scale – greatly magnified so we can see it here! Lyman Lines n=1 Ground State = Lowest Energy Level This emission from a small number of H-atoms is very weak, but hydrogen is very plentiful in space. We see lots of this radiation from our Galaxy and others. (Line first detected in 1951) Note – the lifetime of the 21-cm hydrogen upper state is about 107 yrs, whereas the lifetime of the n = 2 state is 10-9 seconds! A2290-11 A2290-11 21-cm emission E = 6x10-6 eV Atoms and Spectra 20 10