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Lecture 11 Matter and Light Astro161 – Fall 2011 Dr. Matthias Dietrich Homework The second home-work assignment is available after class today and it is also posted on the class web-site, as well as on Carmen. It will be due on Monday, Oct. 24th . The home work has to be returned either in class or as e-mail: [email protected] [email protected] some announcement This Friday, October 21st, will be the second midterm. On Thursday, Oct. 20th, there will be a review session in the planetarium on the 5th floor of Smith Lab at 5pm. A practice test is posted, again on the class web-site and also on Carmen. Smith Lab. 5th floor Planetarium Oct. 03 Oct. 04 Oct. 05 Oct. 11 Oct. 12 Oct. 13 Oct. 17 Oct. 18 Mon. Tue. Wed. Tue. Wed. Thu. Mon. Tue. done done done done done done @ 6:00 pm @ 6:00 pm Roof Nights Oct. 06 Thu. 8:00 pm done Oct. 19 Wed. 8:00 pm (Oct. 26) Lecture 11 Matter and Light In the late 17th and early 18th century experiments with prisms and slits – dispersion and diffraction – lead to the picture that light can be described as a wave phenomenon. Particle ? Wave ? 6 Properties of Waves wavelength • Light waves are characterized • by three numbers: – wavelength, λ (size of the wave) – frequency, f (number of waves/second) – wave speed, c (the same for all wavelengths) • These are all related by: c=λf • longer wavelengthLecture means 2: Lightsmaller frequency The Black Body Radiation Curve Wien’s Law T = 10000 K T = 6000 K 0 5000 Stefan - Boltzmann Hotter blackbodies: • emit more energy at all wavelengths • peak at shorter wavelengths 10000 Wavelength (Å) 15000 20000 9 The Doppler Effect • Shift in the observed wavelength when the source is moving relative to the observer. • Examples: – Sound Waves (Siren or Train Horn) – Light Waves • Amount of the shift and its sign depends on • relative speed of the source and observer • direction (towards or away) Lecture 2: Light The Doppler Effect for Light • Amount of the shift depends upon the emitted wavelength (λem) and the relative speed v: • If the motion is away from observer • Wavelength gets longer = REDSHIFT • If the motion is towards the observer • Wavelength gets shorter = BLUESHIFT Lecture 2: Light Way to Measure Speeds • Observe the wavelength (obs) of a source with a known emitted wavelength (em) • The difference is directly proportional to the speed of the source, v: rest frame 5050Å – 5007Å ·c v = 0.0086 2575 km/s 5007Å observed (For v very small compared to the velocity c of light) Doppler Effect in Practice • Used by astronomers to measure the speeds of objects towards or away from the Earth. • Other Uses: • Traffic Radar Guns: – Bounce microwaves or laser light of known wavelength off of cars, measure reflected wavelength: Doppler shift gives the car’s speed. • Doppler Weather Radar: – Bounce microwaves off of clouds, measure speed and direction of motion. Strength of the reflected signal gives the amount of rain or snow. 13 Doppler Effect and the Shifts of Wavelength – shift to the red if the object is moving away – shift to the blue if the object is moving closer – a way to measure speeds at a distance e.g. how fast a star or galaxy moves away or how fast a car is moving Analysis of Light • Energy which is emitted • Temperature of a body, e.g. a star • Motion of an object along the line of sight Lecture 2: Light What is Matter ? First Ideas • Greek philosophers e.g. Democritus (~460 – ~370 BC) ‘Matter consists of tiny particles (Greek atomos) which cannot be further divided and they have already the properties of the matter they build.’ Ernest Rutherford (1910): Experiments to get an idea about the internal structure of atoms. Most of the mass is concentrated in a compact nucleus smaller than 10-15 m and containing at least 99.98% of the mass which is surrounded by negatively charged electrons. α-particles radioactive material Rutherford’s Model of an Atom not in scale! This only a simple model to provide a sort of picture of an atom. But remember, this is only a picture which tries to visualize an atom. Just to illustrate the size and emptiness of an atom imagine: the size of the Sun is scaled down to the size of the nucleus of an atom (~10-15 m). The electrons would move around the nucleus (~10-10 m) in a distance which would correspond to ~25x the distance of Pluto to the Sun. Electrons don’t orbit around the nucleus like planets around the Sun. Electrons, protons, and neutrons are not little particles but they have particle and wave properties like light. WRONG How do we know all this? Particle accelerator for example CERN near Geneva. ~9 km Underground there are labs with huge detectors which record the decay of particles which are created when for example protons or electrons collide head-on. Atomic Structure Whereas the gravitational force is always attractive, the electromagnetic force can be attractive or repulsive because charges come in two types (positive and negative): – opposite charges attract ✚ – like charges repel ✚ ✚ Atomic Structure • Atomic Structure – Atoms are formed by the electromagnetic force q1 - r q1q2 F 2 r Coulomb Law + q2 Atomic Structure • The atomic nucleus (size ~10–15 m) consists of two types of particles of nearly equal mass: – Protons (positive electric charge) – Neutrons (no electric charge) + Atomic Structure • The atomic nucleus (size ~10 –15 m) consists of two types of particles of nearly equal mass: – Protons (positive electric charge) – Neutrons (no electric charge) • The atomic nucleus is held together by the strong nuclear force, the strongest force in nature, but with a very short range. The Strong Nuclear Force Electromagnetic repulsion F 0 r Strong nuclear attraction, a very short-range force Principal Subatomic Particles Name Size Mass Charge Electron (e–) Proton (p+) Neutron (n) Photon Point? –1 - m 9.1 × 10–31 kg (= 1 me) 1836 me +1 + m 1838 me 0 0 0 10 10 –15 –15 -------- Important Atomic Nuclei • Hydrogen (H) – 1p, 0n – Weight = 1 + Important Atomic Nuclei • Hydrogen (H) – 1p, 0n – Weight = 1 • Deuterium (D) – 1p, 1n – “heavy hydrogen” – Weight = 2 + + the isotope of hydrogen Important Atomic Nuclei • Helium (He) – 2p, 2n – Weight = 4 + + Important Atomic Nuclei • Carbon (C12) – 6p, 6n (common) – Weight = 12 Other isotopes have different numbers of neutrons C13 (7n) C14 (8n) + + + + + + latest count – 116 elements Atoms Massive nucleus held together by strong nuclear force. Electrons “orbit”, held by electromagnetic force. cloud of electrons nucleus - + + number of electrons equals number of protons - Ions Ions are “charged” Atoms, i.e. number of e- number of p+ Here two protons and only one electron + + positively charged ion - Molecules Molecules are collections of atoms that “share” electrons. Molecules are held together weakly by the electromagnetic force. H2 Hydrogen Helium Oxygen Neon Iron Atomic Structure Niels Bohr (1885 – 1962) postulated: • Electrons are allowed only in certain orbits which have specific energies. • Electrons can change orbits by gaining or losing fixed amounts of energy. • This can be done by absorbing or emitting a photon of the correct energy. The Atomic Model by Niels Bohr Electrons are allowed only on discrete orbits with specific energies. Transitions between the orbits require discrete excitation energies. Balmer discovered that for hydrogen the wavelengths for specific transitions are given by Emission/De-excitation An electron drops to a lower-energy orbit, emitting a photon. photon Before After Absorption/Excitation A photon is absorbed, the electron goes to an excited state. photon Before After Absorption/Re-Emission Sequence Photoionization A high-energy photon can remove an electron from an atom. high energy photon Before After Cooling by Collisions • Since photons can carry away energy, photon emission can cool a hot gas. – Temperature is a measure of average speed of particles in the gas. Cool Gas Hot Gas Slow Average Speeds Faster Average Speeds Step 1: Two high-speed atoms collide. Step 1: Two high-speed atoms collide. Step 2: Some of collision energy is used to excite electrons. Exchange of kinetic for internal energy. Step 1: Two high-speed atoms collide. Step 2: Some of collision energy is used to excite electrons. Exchange of kinetic for internal energy. Step 3: Atoms de-excite, losing energy to photons, which escape. Cooling by Collisions • The net result of the collision is that the particles are moving slower (so average speed of gas particles and temperature decreases) and photons carry away energy. • Energy is conserved, but converted from one form (gas kinetic energy) to another (photons). Atomic Structure • Energy levels (allowed orbits) are different for each ion. Depends on the following: – Primarily on number of electrons – Secondarily on number of protons – To a small extent on the number of neutrons • Each element has a unique signature (like a fingerprint) Model Hydrogen Atom Infrared Visible UV Atomic Line Spectra Hydrogen Helium Sodium Mercury If atoms are densely crowded, energy levels are perturbed by neighboring charges Atomic Structure • If atoms are densely crowded, energy levels are perturbed by neighboring charges random shifts of energy levels random shifts of photon energies broadening of spectral lines Low Pressure Medium Pressure High Pressure Solid, Liquid, or Dense Gas Atomic Structure • If atoms are densely crowded, energy levels are perturbed by neighboring charges random shifts of energy levels random shifts of photon energies broadening of spectral lines • Solids, liquids, and very dense gases emit continuous spectra What can we learn from analyzing light ? • Temperature (Kelvin Scale) – measures internal energy content. • The size of an object (L = 4πR2 σT4) • Kirchoff’s Rules of Spectroscopy Kirchhoff’s Rules Kirchhoff’s rules are a set of empirical guide lines that tell us what happens when light and matter interact. 1 a hot dense object produces a continuous spectrum 2 a cool diffuse gas in front of a hot source produces an absorption spectrum 3 a diffuse gas seen against a dark background produces an emission-line spectrum Continuous Spectrum Hot Continuum Source Emission-Line Spectrum Cool, Diffuse Gas Cloud Absorption Spectrum Absorption-Line Spectrum • Light from a continuous spectrum through a vessel containing a cooler gas shows: – A continuous spectrum from the lamp crossed by dark “absorption lines” at particular wavelengths. – The wavelengths of the absorption lines exactly correspond to the wavelengths of emission lines seen when the gas is hot! – Light is being absorbed by the atoms in the gas. Emission-Line Spectra • 19th century: Chemists noticed that each element, heated into an incandescent gas in a flame, emitted unique emission lines. • (Fraunhofer, Bunsen, Kirchoff) – Mapped out the emission-line spectra of known atoms and molecules. – Used this as a tool to identify the composition of unknown compounds. – They did not, however, understand how it worked. Next Telescopes