Monday Feb. 14Syllabus and class notes are at: www.as.utexas.edugo to courses, AST301 – Introduction to Astronomy – LacyThe first exam is Friday, Feb. 18It will cover Chapters 1-6.Reading for this week: Chapter 7 (especially 7.3)If you want help on anything covered in the course, cometo discussion session Thursday at 6:00 in RLM 15.216B.Topics for last week and todayWhat is a photon? What is an electromagnetic wave?How are the photon and wave pictures of light related?Make a sketch of an atom, showing its parts.How do the wave properties of electrons result in onlycertain electron orbits being allowed in an atom?How does the fact that only certain electron orbits canoccur result in photons of only certain wavelengthsbeing emitted?Describe emission and absorption line spectra and theconditions under which each occurs.Describe black body radiation and the relations betweentemperature and the power emitted and thewavelengths of light emitted.Describe the Doppler shift.ProportionalitiesThe circumference of a circle is C = 2 π r.Because there is a C on the left and an r on the right (withno powers on them), we can write C α r.This means that if one circle has twice the radius of another,its circumference is twice as large.Note that proportionalities are always used to compare twoobjects or two situations.QuizHow does the circumference of the big circle compare tothat of one of the small circles?A. _ as bigB. the sameC. twice as bigD. four times as bigQuizHow does the area of the big circle compare to that of oneof the small circles?A. twice as bigB. four times as bigC. six times as bigD. eight times as bigQuizHow does the volume of a sphere whose outline is shownby the big circle compare to that of a sphere outlined byone of the small circles?A. twice as bigB. four times as bigC. six times as bigD. eight times as bigVolumesThe volume of a sphere is given by: V = 4/3 π r3.But you don’t have to know that for this class.You only have to know that there is an r3 in the formula,because all volumes go as width cubed.The diameter of Jupiter is about 1/10 that of the Sun.How do their volumes compare?They are made of the same stuff, packed about equallytightly.How do their masses compare?Energy and PowerEnergy is a measure of how hot something is, or how fast itis moving, or how high it is, or if you burned it how muchheat it would generate.The Joule is one unit of energy. The calorie is another.Power is the rate of flow of energy.That is, how much energy goes into an object each second.A 100 Watt light bulb uses 100 Joules of electrical energyeach second. That electrical energy is converted into100 Joules of light and heat energy each second.One Watt is one Joule per second.Power emitted by a hot objectThe formula for the power emitted by a hot object is:P = (surface area) x σ T4σ is called the Stefan-Boltzmann constant, but you don’thave to know that for this course.I will always ask you questions comparing two objects.Then you can write P α T4. (If they have the same areas.)This formula means that if one object is 3 times hotter thananother, it emits 34 = 81 times as much power.Or if it is 1/3 the temperature of another it emits(1/3)4 = 1/81 as much power.QuizIf Vega (the brightest star in the summer sky) has twice thesurface temperature of the Sun, and if they have thesame size, how does the light power emitted by Vegacompare to that emitted by the Sun?A. Vega emits twice as muchB. four times as muchC. eight times as muchD. sixteen times as muchQuizIf Vega (the brightest star in the summer sky) has twice thesurface temperature of the Sun, and if they have thesame size, how does the light power emitted by Vegacompare to that emitted by the Sun?A. Vega emits twice as muchB. four times as muchC. eight times as muchD. sixteen times as muchWould you have gotten it right if I had said the Sun’stemperature is 6000K and Vega’s temperature is12,000K?Emission line spectraHot gas emits light of only certain wavelengths.If a source emitting a continuous spectrum lies behind coolgas, the gas absorbs some of the light, and it absorbsthe same wavelengths of light that it would emit if hot.To understand why gasses act this way, we need tounderstand more about how electrons orbit in atoms.What is an atom?A hydrogen atom has one proton at its center, with oneelectron orbiting around the proton.The proton has a positive electrical charge.The electron has a negative charge and is about 2000times less massive than the proton.Opposite charges attract, with a force law like that forgravity, so we expect the electron orbit to obey laws likeKepler’s laws.Other atoms have additional protons in their nuclei andadditional electrons orbiting around their nuclei.The also have neutrons (electrically neutral particles withmasses similar to proton masses) in their nuclei.Electron wavesWe normally think of electrons as particles.But like photons, they have both wave and particleproperties.The height of the wave describes the probability of findingthe electron in different places.The wavelength of the probability wave is related to theelectron speed, v, by:λ = h / mv,where h is Planck’s constant and m is the electron mass.In an atom, an electron must orbit at a distance from thenucleus so that an integral number of probability wavesfit around its orbit.This causes only certain electron speeds or energies to beallowed.Emission and absorption of light by atomsWhen an atom absorbs light, the photon energy must equalthe energy needed to make an electron jump from asmall orbit to a bigger one.When an atom emits light, a photon is created, and theenergy of the photon must equal the energy lost by theatom when an electron jumps from one orbit to another.A big jump for an electron requires a high energy photon,or short wavelength light.Doppler shiftIf an object emitting light (or sound) waves is movingrelative to an observer, the observed wavelength isdifferent from that emitted.If the emitter moves toward the observer (or the observermoves toward the emitter) the observed wavelength isshorter than the emitted wavelength.If the emitter moves away from the observer, the observedwavelength is longer than the emitted wavelength.If the motion is small compared to the speed of the wave(the speed of light for light waves) the formula for theshift in wavelength is:(λobserved-λemitted) / λemitted = v /
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