Rainbows and Atoms

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Rainbows and Atoms

Visible Spectrum• To understand Stars & Planets we need spectra• Prism splits Visible light into Visible Spectrum• Newton discovered that white light is made up ofmany colors in 1666• Newton thought light was corpuscles/particles• Young and others showed light was a wave

Electric Field• Electrons & Protons are thenegative & positively chargedelementary particles• They are surrounded by anelectric field• Which changes as they move

Electromagnetism• Changing electric fields (currents) make magnetic fields• Changing magnetic fields make electric currents• Changes in one induce changes in the other Maxwell 1860

Waves Have a Frequency f, Period P,Wavelength λ (lambda) & Amplitude• Frequency countswaves• Frequency = 3 cycles/sec or 3 Hertz• Has 1/3 sec. period• Period of 1 second• Frequency of 1 cycle/sec= 1 Hertz• Has three timeswavelength λ• Both have same heightor Amplitude

Electromagnetic Waves Move atthe Speed of Light c• C= λ f The distance between waves times the number of waves• frequency f =ν=nu• If c=300,000km/sec and the ‘The Q’ has frequency of100Megahertz, what is the wavelength λ?

Electromagnetic Spectrum

Radio Waves• Hertz discovered radio waves in 1888• Marconi and Tesla made first radio• First radio telescope built by KarlJansky 1932

Microwaves• WIFI & Microwave ovens usewavelengths of ~10cm - 2.4GHz• 15meter JCM Telescope studiesinterstellar dust gas, solar system& distant galaxies• Atacama Large Millimeter Arraymost expensive ground basedtelescope

Infrared Region• Bag is transparent to IR light(=heat) - Glasses are not

Ultraviolet Region• FUSE studies very hot stars and gas• SOHO studies the sun

X-ray Region• First discovered by Roentgen in 1895• Wife’s hand with wedding ring• Produced by gas at 10 million Kelvin• NuSTAR X-ray telescope 2012, hasfound 10 supermassive black holes

Gamma γ-Rays• Produced by very hot gas fallingonto a neutron stars & black holes• Produced by radioactive elements

Cosmic Rays• Very high energy subatomic particles• Raining down on us from all directions –no big worry• Unknown production mechanism• AMS-02 on ISS 2010, no Dark Matter yet

A-toms = Not Cutable• To understand light we need Atoms• Democritus 420BC popularized thetheory matter was made of Atoms:• Too small to be seen• Indivisible - Solid• Surrounded by a void• No internal structure

Pictures of Atoms• 48 iron atoms on copper• Made with a scanning tunnellingmicroscope

Temperature• Temperature is a measure of the average kinetic energyof the atoms in gas, liquid or solid = speed of atoms• Animation is of Helium atoms at 20C & high pressure.• Speed of 1500 km/hr slowed down two trillion fold withsome colored red to make them easy to see

Heat = Thermal Energy• The hotter it is; the faster its atoms move• The amount of heat or thermal energy dependson temperature AND mass/number of atoms• The atoms cease moving at absolute zero =zero Kelvin (record=0.45nK)• Bowtie nebula -272C=1K

Brownian Motion Shows Atoms Exist• Microscopic view of milk fat droplets moving randomly due toimpacts from molecules of water – higher temperature faster motion• Einstein published mathematical explanation in 1905

The regions of the electromagneticspectrum in order of increasingfrequency are:a) Radio, microwave, infrared, visible, UV, Xray, γrayb) γray, Xray, UV, visible, infrared, microwave, radioc) Radio, infrared, visible, Xray, UVd) γray, infrared, microwave, radio, UV, visible, Xraye) Xray, UV, radio, microwave

Coming 25Oct13 to the IMAX

Blackbody/Thermal Radiation• A blackbody is opaque = stars, incandescent light bulbs• Radiative properties (spectrum) depend only on temperature• When charged particles are accelerated they emit photons

Blackbody Curve• Because the particles are going different speedsthe photons have a range of energies• Text has wavelength reversed

Wein’s Law• As temperature increases there’s more collisions & more violent ones• So more photons AND more energetic photons• Higher the temperature, the shorter wavelength of peak emission• So higher temperature = bluer color

Stefan-Boltzmann Law• E= σ T 4• Total amount of energy radiated is proportional totemperature to the fourth power• Twice the temperature give 2X2X2x2=16 times the energy

Blackbody Curve• After attempts by Wien, Stephan, Boltzmann, Rayleigh …• Max Planck finds equation (1900) which matches - BUTenergy must be quantized => Quantum Mechanics

Stellar Energy Distributions• Star temperatures vary from 100,000K to 1500K• Maximum of the curve tells us star’s temperature• Albireo composed of hot blue star & cool red one

Planet Impact?• Star HD172555 has a very bright disk• Disk has spectral signatures ofvaporized rock, lava, gravel and dust• Observations consistent with planetaryimpact

Doppler Effect 1842• Stationary Source• Speed of waves equalsthe wavelength λtimes the frequency f• C=λf

Moving Source• Wavelengths in direction ofmotion are compressed• Wavelengths when sourceis moving away fromobserver are stretched• Speed of source determineshow much stretching

Car Horn

Doppler Effect• V r / C = (λ - λ o ) / λ o = Δ λ/λ o• If the source is receding (moving away) then it is a redshift• If the source is approaching then the light is blueshifted

Relative Motion• Stationary observer sees wave with emitted wavelength• Moving observer sees wavelength decreased due to his relativemotion

Transverse & Radial Velocities• We can measure the radial velocity of objects on the other sideof the universe but• We can measure the transverse velocity of only nearby stars• Thus we can only measure the true velocity (true space motion)of the nearby stars

What’s an Atom?-Nucleus & Electron(s)• Rutherford (1911) fired helium nuclei atgold foil and a very few bounced straight back• Nucleus is 100,000 times smaller than the atom• Nucleus of atom is like pinhead in a Stadium

Electrons• JJ Thompson discovers the electron (1897)• Cathode Ray Tube = TV

Number of Protons in Nucleusdetermines Element

• Nuclei containing the same number ofIsotopes protons but a different number of neutrons• Same chemistry BUT different mass• Many are radioactive – medical isotopes

BohrAtom1913• Tiny positive nucleuscontains protons &neutrons and most of mass• “Orbited” by negativelycharged electron(s)• Held in orbit by Coulomb=Electromagnetic Force

Quantum Mechanics• Because electron orbits; it accelerates; it should radiate photons• But energy is quantized so only certain orbitals/energies allowed(just like stairs, piano keys, bookshelf)• Electron can be in lowest energy(=ground state) or in a higher energylevel (=excited state)

Photon Emission/Absorption• When a photon is absorbed,the electron jumps to a higherenergy level = absorption• Excited state• When a photon is emitted, theelectron jumps to a lowerenergy = emission• Ground state• Difference in energy of thetwo states equals energy ofphoton

Electron Cloud• Because an electron is a wave as well as a particle we can notsay exactly where it is due to its quantum mechanical nature• Heisenberg’s uncertainty principle “you can’t know everythingabout anything”

Transitions of Hydrogen• Difference in energylevels determinesphoton energy=wavelength = color• More energy =Bluer color• Balmer series invisible region ;Hα-Alpha, Hβ-Beta,Hγ-Gamma

Absorption SpectrumMatchesEmissionSpectrum

èèKirchhoff’s Lawsçç• Continuous – solid, liquid or dense gas will radiate at all wavelengths• Emission - a low density gas will emit light at specific wavelengths• Absorption - results from a continuous spectrum passing through alow density gas resulting in dark spectral lines

Photon Absorptionand Emission• Usually electron can stayin excited state for~nanosecond• If electron is boosted to 2 ndexcited state it may fallfirst to 1 st excited state andthen to ground state• Emitting 2 lower energyphotons• If electron gains enoughenergy to leave atom it isan Ionized atom

Spectra of Elements• More protons = more electrons & different energy levels• Each element has its own spectrum - like a bar code

Solar Spectrum• Fraunhofer discovered lines insolar spectrum 1817• D=Sodium, C&F&h=Hydrogen,H&K=Calcium

Cecilia Payne-Gaposchkin• Found the abundances of the different elements of the stars• First PhD in astronomy from Harvard/Radcliffe 1925• First woman full professor at Harvard and chair in 1956

Composition of StarsLine strength and line profile depend on abundance of elementAnd temperature (which energy levels are populated)Sun is composed of:Element MassHydrogen 71%Helium 27%All the Rest 2%Most other stars SAME as sun!

Which of the following is NOT oneof Kirchhoff’s Spectral Laws?a. A luminous solid or liquid or dense gas emits lightof all wavelengths producing a continuous spectrumb. A low density hot gas emits light whose spectrumconsists of bright lines = emission spectrumc. A cool thin gas absorbs certain wavelengths from acontinuous spectrum leaving dark absorption linessuperimposed on the continuous spectrumd. For every action there’s an equal & oppositereactione. All of the above

A hotter opaque object:a) Like a hot star will appear bluer than coolerredder star (Wein’s Law)b) Will emit more energy summed over allwavelengths according to Stefan’s Lawc) Will look brighter at all wavelengths according toPlank’s curved) Will be called a blackbody emitting thermalradiatione) All of these

Annie Jump Cannon• Originated the modern stellarclassification scheme in 1901• Based on strength of H lines• Found to be temperature sequenceClassified 400,000 stars forthe Henry Draper Catalogs

Balmer Thermometer• Balmer lines originate at the n=2 energy level• If it is too cool then all atoms in n=1 level• If it is too hot then all hydrogen atoms are ionized• Use Calcium, Helium and molecules as well

Electromagnetic Spectrum• All electromagnetic radiation travels at the speed of light• Energy of a photon depends on frequency/wavelength• Light has both wave and particle properties• Electrons and protons have both wave & particle properties• Everything has wave properties so: Heisenberg uncertaintyprinciple “You can not know anything exactly”

Light is a Particle: A Photon• Einstein showed light is quantized (1905).• Each quantum of light is called a photon• Planck`s constant relates the energy of a photon to frequency. E=hf• Photons are like money; Radio photons are pennies, X-rays-dollars

Spectra ofMolecules• Carbon Monoxide has• A) Electronic transitions• B) Rotational transitions• C) Vibrational transitions• Spectrum of Hydrogen molecule in (a)• Spectrum of Hydrogen atoms in (b)

Thermal Broadening


Discovering Extrasolar Planets• Spectra from largest telescopes have enough precision tosee radial velocity variations of star moving around centerof mass• First was 51 Peg in 1995• Big close planets easiest• Called Hot Jupiters

Energy LevelDiagram of aHydrogen Atom-If an electron gains more than thebinding energy then it willescape from the atom-This process is called ionization- The atom is a positive ion- Denoted by H +- Called a negative ion if it gainsan electron H -

Spectral Classes / Spectral Sequence• Oh Be A Fine Girl/Guy Kiss Me• Spectral Types have subdivisions of 0-9• Pick a star to be representative/standard star

Turbulent Line Broadening

Pressure• Gas is made of tiny atoms & molecules which are in constant motion• The higher the temperature the faster the particles move and• The more often the gas atoms hit the wall the larger the pressure• Bubble nebula – star wind exerts pressure to expand nebulaCoolHot

Pressure/Collisional Broadening• Spectra of Vega & Deneb

Relative Radii of Atoms• Atomic radii are all about 0.1-0.2 nanometer• Smaller than the wavelength of visible light

Radioactive Decay of Carbon 14• Isotopes have same chemical properties• 1 Carbon 14 = 14 C in 10 13 carbon atoms• Half the Carbon 14 will decay in 5700 years• Your body is radioactive (thousands ofdisintegrations/second)

Clocks in Rocks• Clocks start at time of solidifying and reset by melting•238U decays to 234 Th → 206 Pb with half-life of 4.5billion years• We have rock samples of the Earth, Moon, Mars, meteorites• All date to a maximum of ~4.6 Billion years• Time of formation of Solar System

Time to Solar System Formation• Meteorites with chondrules (spherical) formed before Earth• White Calcium Aluminum inclusions were formed 4.57 billion years• Short lived radioactive elements indicate that ~million years elapsedfrom supernova/solar system formation and rock crystallization

Atom• Number of Protons determines the Element• Neutrons hold the nucleus together• Number of electrons determined by protons in nucleus• Chemistry determined by electrons

Star’s With Dust Disks• Star radiates light like ahot Blackbody• Some starlight warmsthe disk• Disk radiates light(Infrared) like a coolerBlackbody

Spectral Sequence = Temperature Sequence

Spectrum of a Nebulae

Solar Spectrum• Millions of absorption lines of different elements and ions• Width of lines depends on temperature and abundance

Kirchhoff’s Laws=Kinds of Spectra

Types of SpectraWe usually look at graph of Intensityversus Wavelength• No lines = Continuous• Absorption lines = Dark lines• Emission lines = Bright Lines

Hydrogen Energy Level Diagram• Lyman Series• Balmer Series• Paschen Series• Ion, Ionized, Ionization and Binding energy• Recombination

(B-V) Color Index• Counting the number of photons which pass through a filter andcomparing to another filter will tell us the temperature of a star• A hot blue star has a (B-V) = -0.1 and (B-V)=1.5 for a cool red star

Carbon Atom in Ground State• Six electrons populatingmany energy levels givesmuch more complexspectrum

Wien’s Law• Wavelength of maximum intensity depends on temperature• λ = 3,000,000/Temp in nanometers & degrees Kelvin• λ = 3,000/Temperature in microns & Kelvin

Image/Line Spectra• We rarely look at bands of color• Usually we graph intensity versus wavelength

Loss ofAtmosphere• First atmosphere of Hydrogenand Helium• Is lost to space because thetemperature / velocity is abovethe escape velocity

Neutrons & Isotopes

Waves• Wavelength λ is distance betweencrests• Frequency f is number of wavesper second which pass a point

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