Chapter 2

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Chapter 2

Wavelength (λ) (Unit of length: m, cm, nm, …)• Distance between successive wave peaksPeriod (Units of time: s)• Time between the passing of wave crestsFrequency (f)• Number of “vibrations” per unit time(Unit: Hertz, Hz = 1/s). Multiples: kHz, MHZFrequency = 1/ PeriodWave Speed (Units of velocity: km/s, m/sec)• Wave Speed = Wavelength x FrequencyIn the case of light :c = wavelength x frequencyc = λ x fλ = wavelength (lambda)f = frequencyImportant: Light at all wavelengths travels in vacuum at the samespeed: c = 300,000 km/s


Electrically charged particles andelectromagnetic wavesElectrons havechargeProtons have + chargeBoth have electric fields+ attract,++ and repel• The changing position of a chargedparticle creates “waves” calledelectromagnetic waves• The electromagnetic wavestravels through empty spaceeventually interacting with a distantcharged particle.• Visible light is anelectromagnetic wave


MagnetismMoving electric charges alsoproduce Magnetic fields.Example: electric currentpassing through a coil.Another example: electricmotorsAnother interestingexample:The Earth’s magnetic fieldis produced by thespinning of charges in theliquid metal core of theEarth.Conversely,magnetic fields forcecharged particles tomove….


Accelerated charges (electrons, protons) produce:Anelectromagneticwave iscomposed of twooscillating fields,an electric fieldand a magneticfieldperpendicular toeach otherRipples in the ElectroMagnetic (E&M) field= E&M Waves = LIGHT!


Wavelength means COLOR400nm 500nm 600nm 700nmVisible light ranges in wavelength from~400 to ~700 nanometers.


Electromagnetic SpectrumMicrowaves,cookingcommunicationheatdetected byour eyessunburnpenetratetissuemostenergetic


Visible lightis a smallpart of theEMspectrum.


Did you ever wonder why astronomers puttelescopes on mountaintops or in space?


The temperature scaleComparison of Kelvin, Celsius and Fahrenheit scalesThe scale most used in sciences, physics and astronomy is Kelvin.The unit is kelvins (K)


• The atoms and molecules thatmake up matter are in constantmotion.• The temperature of an objectmeasures the amount ofmicroscopic motion of theparticles.•The kinetic energy is E = ½ m v²• The higher the temperature, thefaster the particles move and thelarger the kinetic energy.Blackbody Radiation•When the charged particleschange their state of motion,electromagnetic radiation isemitted.


Thermal RadiationBlackbodies, like stars, light bulbs and irons, emit thischaracteristic spectrum of light.The intensity peaks at a given frequency and fall off to lesservalues above and below that frequency.Blackbody Spectrum:


Blackbodies with different temperatures look like this:Hotter blackbodies are brighter and “bluer.”(nm : nanometer; 1 nm = 10^-9 m)


Wien’s Law• Hotter bodies radiate more strongly at shorter wavelengths(i.e. they’re bluer).• Cooler bodies radiates more at longer wavelengths (i.e.they are redder)• There is a wavelength at which the intensity of theradiation reaches a maximum ( max )max =0.29 cmT (K)Using this equation we can measure a star’s temperaturefrom its spectrum!


Stefan’s Law• “Hotter blackbodies are brighter overall (atevery wavelength).”where: F = total radiative flux (total energy radiated per second)= constantF = T 4The total radiated flux or total energy radiated per second isproportional to the area under the black body curveAlso note that the total energy radiated per second is proportional to thefourth power of an object’s temperatureIf the temperature T of a body is increased to 2T, the total energyradiated per second is increased to (2T)^4 = 16 T^4


Application of Stefan’s and Wien’s LawsStefan’s LawDoubling the temperature from6,000 K to 12,000 K of a blackbody will increase the totalradiated flux (Total energy radiatedper second) by a factor of 16The total radiated flux isproportional to the area under thecurve. The area under the 12,000K curve is 16 times larger than thearea under the 6,000 K curveWien’s Lawmax =242 nmmax = 2,900,000 nm/ T (K)The max shift from the visual,around 483 nm (green-yellow) toaround 242 nm (ultraviolet).The plot is in linear scalemax =483 nm


(Flux)Thetemperatureof the starsand the Sun


Stellar Colors• Reddish coolest stars (~3000 K)• Orange-ish• Yellowish• WhiteSun (~6000 K)• Bluish hottest stars (~50,000 K)• Stars, light bulbs, irons, etc., are ~Blackbodies withdifferent colors, depending on their temperature.• A Blackbody is a perfect emitter and absorber, whosetemperature defines how much light it emits at eachwavelength.


Comparison of blackbody curves fromfour astronomical objectsBinary Star Albireo, Beta CygniFor the Gator fans: The Gatorstar !Temperature orange star = 4,080 KTemperature blue star = 13,200 K


Spectroscopy(Analysis of Spectra)• Light can be separated into different wavelengths(separated in colors) to produce a spectrum.• The instrument used to produce and analyze a spectrumis known as a spectroscope• It consist of a opaque barrier with a slit to produce anarrow beam of light, a prism or a diffraction grating anda detector (it can be the eye) or a screen to project thespectrum.


Continuous Spectrum


Emission Line Spectrum


Emission Line SpectraEach element produces its own unique pattern of lines


Absorption Line Spectrum


Absorption Line SpectraSpectrum of the SunThe H (Hydrogen) letter followed by a Greek letterare used for the Balmer series (Visible H lines).


Three Types of SpectraContinuousEmission LinesAbsorption Lines


Kirchhoff’s Laws of Radiation(Published in 1859)Kirchhoff’s First Law• Hot, dense gases or solids produce acontinuous spectrum.• Emits light at all wavelengths• Example: Light bulb filamentContinuous Spectrum


Kirchhoff’s Second Law• A hot, low-density gas when exited (Electriccurrent, UV emission) produce an emissionline spectrum.• These lines are characteristic of the chemicalcomposition of a gas• The lines are the “fingerprints” of the chemicalelement. They are unique to the element.• Examples: Neon signs, Sodium vapor street lamps,emission nebulaeEmission Line Spectrum


Kirchhoff’s Third Law• A Low-density cool gas in front of a hotcontinuous source produces an absorption linespectrum.• These lines are characteristic of the chemicalcomposition of the gas• For the same gas, the absorption lines occur at thesame wavelengths of the emission lines• Example: The Sun, starsAbsorption Spectrum


Summary of Kirchhoff’s Laws:123How can we explain the discrete emission or absorption in“lines?”Using Kirchhoff ‘s laws we can describe the phenomenonbut do we have a theory to explain it?


The Nature of AtomsThree subatomic particles makeup an atom:1. Proton - positive charge2. Neutron - no charge3. Electron - negative charge• The nucleus is composed of protons andneutrons.Like charges repel so a large amount of forceis required to keep the protons in the nucleustogether.mass of protonmass of neutron1836 x mass of electronAtoms are mostly empty space! And, since all matter is made upof atoms, matter is mostly empty space!!If an atom loses or gains an electron, it acquires an electriccharge. It is said to be ionized and it is therefore an ion.Atoms can bond with other atoms of the same kind or differentkind to form molecules.


Each atom of a given element contains a specific number ofprotons and electrons thus making that element unique.


Bohr’s Hydrogen ModelNiels BohrIn 1913, Bohr developed a model of the atom that provided thefirst explanation of the hydrogen’s spectral linesp + e - Electron orbits theproton (i.e. nucleus)kept in place by theCoulomb Force (F c ).1F cR2How does this structure lead to uniqueemission and absorption lines?


Bohr’s Model• Electrons can only bein particular orbits(energy states).Excited state(higher energy)Ground state(lowest energy)• Energy is“quantized” (QuantumMechanics).• Excitation requiresenergy to beadded to the atom• De-excitation -energy is releasedfrom the atomep


nucleuselectronsR 1R 2R 3E 1gain energyR 1R 2E 2E 3R 3lose energyE = E 3 -E 1Electron needs to gain energy to move from R 1 to R 3 (excited).Electron needs to lose energy to move from R 3 to R 1 (de-excited).How does the electron get the energy it needs to become excited?1. Collisions between atoms can excite electrons to higher energylevels. Passing an electric current (applying a high voltage to a lowdensity gas)will make atoms collide.2. The absorption of energy from light can excite electrons.


What’s going on?Light can behave as a particle.Albert EinsteinLight energy must be carried in packets called photons.Einstein was awarded the Nobel Prize in 1921 for histheory of the photoelectric effect. The effect can beexplained if light is considered as a particle (photons)• Photon energy•Photon energy1/wavelengthfrequency• Light Intensity = # photonsarriving/second• Low energy photons cannot cause e ejections.• High energy photons cause ejection of e (can ionize an element)


Quantum Mechanics:Atoms can only absorb or emitphotons with energies exactly equalto the energy difference betweenelectron orbits.The energy of a photon is related to the wavelength:E ph 1/ fE ph = h f = h c/(f = c/ )h is the Planck’s constantLarger orbital jumps shorter wavelength photons.(Larger orbital jumps have larger energy levels)Important: A radio photon as long wavelength and low energyA gamma ray photon as short wavelength and high energy


The energy of the photon must be precisely equal to E.E p E E p = EPhotonabsorbedphoton emittedE p = E


The Hydrogen atom• Atoms of different elements haveunique energy level structures. Thefigure on the left, shows some of theenergy levels of Hydrogen• Every e “transition” corresponds toa unique wavelength.• Ionization = ejection of e .• The figure at the bottom shows theBalmer series of Hydrogen. Part of thelines of this series are in the visiblepart of the spectrum.Hydrogen


Examples of spectra of different elements. Every element (atom) emit orabsorb a particular set of lines. It has a unique signature or fingerprint ofthat element


Bohr’s Hydrogen AtomIn modern quantummechanics:Electrons are not just particles,but also waves, without exactlocations.


The Doppler EffectMoving sources, like fire trucks and race cars, change pitch asthey go by.The pitch is higher (Higher frequency) when they are approachingan lower (lower frequency) when they are moving away.This is an example of Doppler effect in sound waves


Doppler effect• Motion along the line of sight (radial motion)produces a Doppler effect• No Doppler effect if the motion is perpendicularto the line of sight


Doppler effect in electromagneticwaves• Electromagnetic waves also has a Doppler effect.• Light emitted by a moving object also present Dopplereffectv/c = Δ / = ( shift - rest)/ restv is the radial velocity of an objectc is the speed of lightΔ = ( shift - rest) is the change in wavelengthshift is the shifted or observed wavelengthrest is the wavelength at rest


The Doppler ShiftStationarysource:Movingsource:


An example of a body emitting the Balmer series of hydrogenRed shift and blue shift of hydrogen Balmer series linesImportant!If the body emitting the Balmer series is receding (moving away fromobserver), the lines are shifted to the red part of the spectrum. Thespectrum is said to be red shifted. The body do not necessarily looks redIf the body is approaching the observer, the lines are shifted to the blue partof the spectrum. The spectrum is said to be blue shifted. The body do notnecessarily looks blue


Obtaining the rotation of an object from the width of the Doppler lines• If an object (a planet, a star or a galaxy) is rotating, the sideapproaching the observer will be blue shifted. The side moving awayform the observer will be red shifted.• The line emitted from the center will have no shift.• As a consequence, the line will be wider that it would if the objecthad no rotation.• The rotation rate of the object can be determined by measuring thewidth of the spectral lines


What can we learn from spectroscopy?• The chemical composition by matching the spectral lines with laboratoryspectra of atoms.• The temperature by matching overall spectral shape with blackbody curve.• The line-of-sight velocity by determining the Doppler shift.• The rotation rate by measuring broadening of spectral line due to Dopplershift.• The pressure of the gas in the emitting region due to broadening of spectrallines. The greater the pressure, the broader the line• The magnetic field (Zeeman effect) which splits a single line into two lines

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