3.5 The Doppler Effect: this is how we learn about the motions ofobjects in the universe, discover extraterrestrial planets, black holes at thecenters of galaxies, and the expansion of the entire universe.4.1 Spectral Lines: appearance, excess or deficit of energy atparticular wavelengths. (Don’t worry about Kirchoff’s laws, and the pictureswith little prisms and light bulbs etc.--see notes)4.2 Atoms and Radiation: quantized energy levels of electrons inatoms, and how they interact with radiation.The hydrogen atom--the simplest, and most important case.4.3 The Formation of Spectral Lines: understandingemission lines and absorption lines4.4 Molecules: not just electronic changes, but vibrational androtational changes of energy.4.5 Spectral-Line Analysis: Information from spectral lines-abundances, turbulent motions, rotation, …Topics through Chapter 43.5 The Doppler EffectThe wavelength (or frequency) of a wave, as measured by an observer, depends on the relativeradial speed of the source and observer.Radial motion means: motion towards or away; along the line of sight.The Doppler effect involves only this component of motion. What we get from measuringit is called the radial velocity.Moving toward: wavelengthsdecrease (“blueshift”)Moving away: wavelengths increase (“redshift”)3.5 The Doppler EffectRelationship between wavelength and speed:! Shift in compared to “rest (no motion) wavelength” is proportional to radialvelocity! So if you know the exact wavelength where some feature in the spectrumshould be (“true wavelength”), and the wavelength at which it appears(“apparent wavelength”), you can obtain the radial velocity.! This is how we get speeds of cosmic objects, stars, galaxies, even expansion ofuniverse.Actual formula is: (apparent)/ (true) = 1 ± (speed of object/speed of light)where the ± sign means it is + if it is moving away from us (redshift, longerwavelength), - if it is moving toward us (blueshift, shorter wavelength)This applies to any wave; and no reason notto use frequency instead of wavelength.Textbook writes it this way:3.5 The Doppler EffectImportant point: Dopplereffect depends only onthe relative motion ofsource and observerSee textbook for this ratherconfusing example. In classwe’ll use a simpler exampleof water waves in a pond.More Precisely 3-3: Measuring Velocities with theDoppler EffectExample: For a speed of 30 km/s, the Doppler shift is given byspeed of lightspeed of objectThis may seem small, but it is easilydetectable with a radar gun.It is NOT so easy to detect fromthe spectrum of an astronomicalobject, unless you know somethingabout spectral lines.Look at the Doppler shift formula again: (apparent)/ (true) = 1 ± (radial velocity of object./speed of light)If velocity of object away or toward us is much less than thespeed of light (true for almost all objects in the universe), the apparentwavelength will be only slightly different from the “laboratory” or “rest”wavelength.For most objects in the universe,this relative shift is so tiny, that wecan’t detect it using the “shift” ofthe whole continuous spectrum.But we can use places in thespectrum whose wavelengths areprecisely known by the presenceof spectral lines (the subject ofChapter 4)Chapter 4SpectroscopyDon’t worry if you can’t understand what this pretty picture represents,unless it is the day beforethe next exam.A more important question Is why the authors insiston showing this form of spectra withoutadequately explaining!Spectroscope: Splits light into component colors(wavelengths, frequencies)4.1 Spectral LinesMost of this illustration is completely unnecessary! The only importantpoint is that light from any object can be spread out into a “rainbow” ofwavelengths. A spectrum is a picture of how much light is at eachwavelength. This illustration is showing a contin uous spectrum.Emission lines:Single frequencies emitted byparticular atoms in a hot gas4.1 Spectral “Lines”Absorption lines:If a continuous spectrum passes through acool gas, atoms of the gas will absorb thesame frequencies they emitContinuous spectrum:Continuous range of frequenciesemitted by an object (something like the“black bodies” we discussed in ch.3)Spectral linesSpectral lines—very narrow, well-defined (in wavelength) wavelength/frequency regions in the spectrum where excess photon energy appears (emission lines) or else where photons are missing (absorption lines). Often these lines are superimposed on asmooth, “continuous” spectrum, which is thenear-blackbody emission of a heated objectthat we have been discussing so far (ch. 3,Wien, Stefan-Boltzmann).Cartoon view of absorption lines, both inthe spectrum as a graph (below), and in therecorded spectrum (top), the band ofcolors--this is just how the spectra aregathered--pay no attention to the rectangularshape!Spectral of real astronomical objectsHere are spectra of two real astronomical objects, a comet (top) and star (bottom).By the time you take the next exam, you should be able to explain why these lookso different. The wavelengths, shapes, and strengths of these “spectral lines” are the keys tounderstanding many of the physical properties of planets, stars and galaxies.Spectra are not black rectangles with vertical lines.They are a recording of how many photons per second are beingemitted as a function of wavelengthEmission spectrumcan be used toidentify elements4.1 Spectral LinesAn absorptionspectrum can also beused to identifyelements.These are the emissionand absorption spectraof sodium:Here is the Sun’s spectrum, along with a blackbody of the sun’s temperature(top--why are there no lines?), and the spectra of individual elements asobserved in the laboratory. Each spectral line is a “chemical fingerprint” tellingyou which elements, and how much of each element, is contained in the objectyou are observing.Continuous spectrumSun (absorption lines)Emission lines ofvarious elementsKirchoff’s laws: don’t memorize them. Instead, come back to thisillustration later and find if you understand enough to explain them“Kirchoff’s laws” are usually presented with prisms and striped colorful “spectra.”This is confusing, and they aren’t even “laws” at all!Just note that “prism” is supposed to represent an instrument, called a “spectrometer.” If the light from the hot “star” or blackbody doesn’t pass through any low-density gas,then the spectrum
View Full Document
Unlocking...