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Taking fingerprints of Taking fingerprints of stars, galaxies, and stars, galaxies, and

interstellar gas cloudsinterstellar gas cloudsAbsorption and emission from Absorption and emission from atoms, ions, and moleculesatoms, ions, and molecules

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Periodic Table of ElementsPeriodic Table of Elements

• The universe is mostly hydrogen H and helium He (97%)• These (and a little lithium, Li) were only elements created in Big Bang

– ALL heavier elements have been (and are still being) manufactured in stars, via nuclear fusion

• Each element has own characteristic set of energies at which it absorbs or radiates electromagnetic radiation

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PlanckPlanck’’s Theory, 1901s Theory, 1901

• Light with wavelength λ has frequencyν = c/λ

• can “exchange” energy with matter (atoms) in units of:

E = hν• h is “Planck’s constant”

h = 6.625 × 10-34 Joule-seconds

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The Bohr AtomThe Bohr Atom• Model of Hydrogen atom

– Introduced by Niels Bohr early in 1913– to explain emission and absorption of light by H

• 1 proton ( “nucleus”) “orbited” by 1 electron

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The Bohr AtomThe Bohr Atom• Electron “orbits” have fixed sizes ─ “orbitals”

– Not Like Planets in a “Solar System”– atomic orbitals are “QUANTIZED”

• only some orbital radii are “allowed”

– was very confusing to physicists– first deduced by physicist Neils Bohr

• Movement of electron e- between orbitals requires absorption or radiation of energy– jump from lower to higher orbital ⇒ atom absorbs energy– jump from higher to lower orbital ⇒ atom emits energy

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Bohr AtomBohr Atom

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Absorption of Photon “kicks” electron to “higher” orbital

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Bohr AtomBohr Atom

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Emission of Photon makes Electron “drop” to “lower” orbital

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Absorption vs. EmissionAbsorption vs. Emission

• Atom “absorbs” photon if electron “kicked” up to a “higher” energy state

• Atom “emits” photon if electron “drops” down to a “lower” state

• Again, only a certain set of energy states is “allowed”– set of states depends on the atom or molecule

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““EnsemblesEnsembles”” (Groups) of Atoms(Groups) of Atoms• Individual H atoms in a group of H

atoms have different states (are in different “orbitals”)– Electrons in some atoms are in “low” states

and are more likely to absorb photons– Electrons in some atoms are in “high”

states and more likely to emit photons• What determines the “distribution” of

states of a group of atoms?

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Ensemble of Atoms in Ensemble of Atoms in ““LowLow””StatesStates

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Ready to Absorb, SIR!

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Ensemble of Atoms in Ensemble of Atoms in ““LowLow”” StatesStates

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Photons from Star at “correct”λ are absorbed, and thus removed from the observed light

Absorption Line

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Absorption Absorption ““lineslines””

• Discovered in Solar spectrum by Fraunhofer– called “Fraunhofer Lines”

• “Lines” because they appear as dark bands superimposed on “rainbow” of visible spectrum

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Ensemble of Atoms in Ensemble of Atoms in ““HighHigh””StatesStates

Ready to Emit, SIR!

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Ensemble of Atoms in Ensemble of Atoms in ““HighHigh””StatesStates

Photons at “correct” λ are emitted, and thus added to any observed light

Emission Line+

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Dark Background

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Emission line spectrumEmission line spectrum

Appear as Bright Bands on “Faint Background Spectrum”Why the Background??

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Some Atoms are in Both StatesSome Atoms are in Both States(but (but ““oneone”” usually dominates)usually dominates)

Absorption & Emission

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More absorption if more atomsin “low” state

More emission if more atomsin “high” state

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Why Would Ensemble of Atoms Why Would Ensemble of Atoms be in be in ““HighHigh”” or or ““LowLow”” State?State?

• Some other mechanism (besides light) must be at work! But what?

TEMPERATURE T

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Effect of Thermal EnergyEffect of Thermal Energy• If T ≈ 0K (ensemble of atoms is very cold), most

atoms are in “low” state– can easily absorb light

• If T >> 0K (ensemble of atoms is hot), the thermal energy “kicks” most atoms into “high”state– can easily emit light

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Sidebar: LASERSidebar: LASER• Electrons in the medium (gas, solid, or

diode) of a LASER are “driven” to “high”state by external energy

• Emit simultaneously and with same “phase”

• External Energy:– electrical– optical (external light source, flash lamp)

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Sidebar: LASERSidebar: LASER• External source maintains “energy

inversion”– more electrons in “high” state, even during

and after emission

high

low

After “Driving” After Emission

EmissionAbsorption

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Geometries for producing Geometries for producing absorption linesabsorption lines

• Absorption lines require cool matter (gas) between observer and hot source– scenario 1: cooler atmosphere of star– scenario 2: cool gas cloud between star and observer

The Observer1

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SunSun’’s Fraunhofer absorption liness Fraunhofer absorption lines

(wavelengths listed in Angstroms; 1 Å = 0.1 nm)

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Geometries for producing Geometries for producing emission linesemission lines

• Emission lines require hot matter (gas) viewed against colder background – scenario 1: hot “corona” of a star– scenario 2: cold gas cloud seen against “empty” (colder) space

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2The Observer

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Emission line spectraEmission line spectra

Insert various emission line spectra here

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What Wavelengths are Emitted What Wavelengths are Emitted and/or Absorbed?and/or Absorbed?

• Depends on Size of “Gaps” between Energy States in the atoms

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Energies of H Energies of H OrbitalsOrbitals

Energies of Orbitals of H

“Transitions” between Orbitals

Limiting Energy

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Ionization of HydrogenIonization of Hydrogen

Limiting Energy

If electron absorbs sufficient energy E to rise above the “upperlimit” of energy for a “bound”electron, then the electron becomes“ionized”• electron “escapes” the proton

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Relate Size of Relate Size of ““GapGap”” to to Wavelength of LightWavelength of Light

• Larger “gaps” or “jumps” in energy (both absorbed and emitted) ⇒ photon carries more energy

• Recall

• Larger ∆E ⇒ Shorter λ ⇒ “bluer” light• Smaller ∆E ⇒ Longer λ ⇒ “redder” light

2 11hcE E E hν

λ λ− = ∆ = = ∝

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Relate Size of Relate Size of ““JumpJump”” to the to the λλ Absorbed or EmittedAbsorbed or Emitted

• Very Small ∆E ⇒ Very Long λ⇒ Radio Waves

• Very Large ∆E ⇒ Very Short λ⇒ X rays

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Sidebar: A Common Transition Sidebar: A Common Transition Very Small Very Small ∆∆E E ⇒⇒ VeryVery Long Long λλ

• Due to “spin flip” of e- in Hydrogen Atom

• ∆E = hc/λ ≈ 9.4 × 10-25 Joules• ⇒ λ ≈ 0.21 m = 21 cm• ⇒ ν ≈ 1420.4 MHz ⇒ RADIO Wave

High-E State Low-E State

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Sidebar: 21Sidebar: 21--cm Radio Wave of Hcm Radio Wave of H

• First observed in 1951– Simultaneously Discovered at 3

observatories!! (Harvard, Leiden, Sydney)

• Measures the H in “interstellar matter”– Map of Spiral Arms in Milky Way Galaxy

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Bohr Atom:Bohr Atom:Extension to other elementsExtension to other elements

• H is simplest atom, BUT concept of electron orbitals applies to all atoms

• Neutral atoms have equal numbers of protons (in nucleus) and electrons (orbiting nucleus)– He has 2 protons & 2 electrons; Lithium (Li), 3 each;

Carbon (C) , 6 each, etc. ...

• More electrons (and protons) ⇒ more complicated absorption/emission spectrum

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Optical EmissionOptical Emission--Line Spectrum of Line Spectrum of ““Young StarYoung Star””

λ (in Angstroms Å, or units of 10 nm)

Inte

nsity

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Emission line imagesEmission line images

Planetary nebula NGC 6543(blue: X Rays)

green ⇒ oxygenred ⇒ hydrogen

Orion Nebula

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Spectra of Spectra of ionsions

• Emission lines from heavy ions dominate high-energy (X-ray) spectra of stars– atoms stripped of one

or more electrons

• Ions of certain heavier elements (e.g., neon and iron with only one electron) behave much like “supercharged” H and He

Wavelength (in Angstroms)

Neon Iron

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MoleculesMolecules• Also have characteristic spectra of emission

and absorption lines– Each molecule has particular set of allowed

energies at which it absorbs or radiates• Molecules are more complicated than atoms

– Spectra are VERY complicated• Electrons shared by one (or more) atoms in molecule

absorb or emit specific energies• Changes in state of vibration and/or rotation are also

quantized– Vibration, rotation spectra unique to each molecule

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Molecular SpectraMolecular Spectra• Transitions between different “orbitals” of

molecules (“electronic” states) (large ∆E)– mostly in ultraviolet (UV), optical, and infrared (IR)

regions of spectrum• Transitions between different “Vibrational”

states (“middlin” ∆E)– mostly in the near-infrared (NIR)

• Transitions between different “Rotational”states (small ∆E)– mostly in the radio region

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Rank Molecular Transitions by Rank Molecular Transitions by EnergyEnergy

1. UV, Visible, IR ⇒ Electronic2. NIR ⇒ Vibrational3. Radio ⇒ Rotational4. Radio ⇒ H “spin flip” @ ν = 1420 MHz

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Molecular Transitions inMolecular Transitions inPlanetary Nebula NGC 2346

Electronic Transition(visible light)

Vibrational Molecular HydrogenTransition (IR)

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Molecular Emission: Molecular Emission: Rotational TransitionRotational Transition

Rotational CO (carbon monoxide) Emission from Molecular Clouds in “Milky Way”

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Q: How to Measure Spectra?Q: How to Measure Spectra?• A: With a “Spectrum Measurer”

– “SPECTROMETER”– “Splits” light into its constituent wavelengths

and measures them• Mechanisms for “Splitting” Light

1. Optical Filters: “Block” light except in desired band

2. “Dispersion” of Glass = “Differential Refraction”- Prism

3. Diffraction Grating

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1. Filter Spectrometer1. Filter Spectrometer

Filters in Rotating “Filter Wheel”Sequence of “Monochrome” Images thru Different Colors(How the images in the laboratory were created)

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Multispectral ImagingMultispectral Imagingused for Manuscriptsused for Manuscripts

ultraviolet 450 nm 550 nm 650 nm near infrared

Multispectral imaging will be used to differentiate between the two inks in the two sets of writing and separate them from the parchment and the mold. The goal is to read the erased writing underneath the obscuring overwriting and also to detect any ink in the moldy regions.

The spectral response of the two inks is visible in this figure. The contrast of both inks decreases for longer, i.e. redder wavelengths, but the erased writing decreases in contrast more quickly.

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2. Prism Spectrometer2. Prism Spectrometer

n

λ

Recall: Optical Dispersion

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2. Prism Spectrometer 2. Prism Spectrometer • “Refractive Index” n measures the

velocity of light in matter

c = velocity in vacuum ≈ 3 ×108

meters/secondv = velocity in medium measured in same

unitsn ≥ 1.0

vcn =

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2. Prism Spectrometer 2. Prism Spectrometer

• Refractive index n of glass decreases with increasing wavelength λ

• Make a glass device that uses optical dispersion to “separate” the wavelengths– a PRISM

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2. Prism Spectrometer2. Prism Spectrometer

White Light In

θBlueθRed

Long λ “dispersed” by smallest angle θ

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2. Prism Spectrometer2. Prism SpectrometerProblems:Problems:

• Glass absorbs some light– Ultraviolet light

• Why you can’t get a suntan through glass– Infrared light

• Images taken in different λ will “overlap”• Dispersion Angle θ is complicated function

of wavelength λ⇒ Spectrometer is difficult to “calibrate”

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3. Grating Spectrometer3. Grating Spectrometer

λ

θ

θRed

λ

θBlue

Different λ Interfereat Different θ

“Interference” of Light

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3. Grating Spectrometer3. Grating Spectrometer

White Light In

Long λ “diverges: atlargest angle θ

θBlue

θRed

Long λ “dispersed” by largest angle θCan be constructed for all wavelengths

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3. Grating Spectrometer3. Grating Spectrometer• Uses “Diffraction Grating”

– works by “interference” of light– Regularly spaced “transparent” & “opaque” regions

• Can be made without absorbing glass– Used at all wavelengths (visible, UV, IR, X-Rays, …)

• Dispersion angle θ is proportional to λ– Easy to calibrate!

• Images at different λ can still overlap