kirchhoff’s laws: dark lines cool gas absorbs light at specific frequencies “the negative...
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Kirchhoff’s Laws: Dark Lines
Cool gas absorbs light at specific frequencies
“the negative fingerprints of the elements”
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Kirchhoff’s Laws: Bright lines
Heated Gas emits light at specific frequencies “the positive fingerprints of the elements”
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Kirchhoff’s Laws
1. A luminous solid or liquid (or a sufficiently dense gas) emits light of all wavelengths: the black body spectrum
2. Light of a low density hot gas consists of a series of discrete bright emission lines: the positive “fingerprints” of its chemical elements!
3. A cool, thin gas absorbs certain wavelengths from a continuous spectrum dark absorption ( “Fraunhofer”) lines in continuous spectrum: negative “fingerprints” of its chemical elements, precisely at the same wavelengths as emission lines.
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Spectral Lines • Origin of discrete spectral lines: atomic structure of matter
• Atoms are made up of electrons and nuclei– Nuclei themselves are made up
of protons and neutrons
• Electrons orbit the nuclei, as planets orbit the sun
• Only certain orbits allowed Quantum jumps!
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• The energy of the electron depends on orbit• When an electron jumps from one orbital to
another, it emits (emission line) or absorbs (absorption line) a photon of a certain energy
• The frequency of emitted or absorbed photon is related to its energy
E = h f
(h is called Planck’s constant, f is frequency)
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Energy & Power Units
• Energy has units Joule (J)
• Rate of energy expended per unit time is called power, and has units Watt (W)
• Example: a 100 W = 100 J/s light bulb emits 100 J of energy every second
• Nutritional Value: energy your body gets out of food, measured in Calories = 1000 cal = 4200 J
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Stefan’s Law
• A point on the Blackbody curve tells us how much energy is radiated per frequency interval
• Question: How much energy is radiated in total, i.e. how much energy does the body lose per unit time interval?
• Stefan(-Boltzmann)’s law: total energy radiated by a body at temperature T per second: P = A σ T4
• σ = 5.67 x 10-8W/(m2 K4)
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Example
• Sun T=6000K, Earth t=300K (or you!)
• How much more energy does the Sun radiate per time?
• Stefan: Power radiated is proportional to the temperature (in Kelvin!) to the fourth power
• Scales like the fourth power!
• Factor f=T/t=20, so f4 =204=24x104=16x104
160,000 x
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Example: Wien’s Law• Sun T=6000K, Earth t=300K (or you!)
• The Sun is brightest in the visible wave lengths (500nm). At which wave lengths is the Earth (or you) brightest?
• Wien: peak wave length is proportional to temperature itself Scales linearly!
• Factor f=T/t=20, so f1 =201=20, so peak wavelength is 20x500nm=10,000 nm = 10 um
• Infrared radiation!
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The Sun – A typical Star • The only star in the solar system• Diameter: 100 that of Earth• Mass: 300,000 that of Earth• Density: 0.3 that of Earth
(comparable to the Jovians)• Rotation period = 24.9 days
(equator), 29.8 days (poles)• Temperature of visible surface
= 5800 K (about 10,000º F)• Composition: Mostly hydrogen,
9% helium, traces of other elements
Solar Dynamics Observatory Video
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How do we know the Sun’s Diameter?
• Trickier than you might think• We know only how big it appears
– It appears as big as the Moon
• Need to measure how far it is away– Kepler’s laws don’t help (only relative
distances)
• Use two observations of Venus transit in front of Sun – Modern way: bounce radio signal off of Venus
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How do we know the Sun’s Mass?
• Fairly easy calculation using Newton law of universal gravity
• Again: need to know distance Earth-Sun• General idea: the faster the Earth goes around
the Sun, the more gravitational pull the more massive the Sun
• Earth takes 1 year to travel 2π (93 million miles) Sun’s Mass = 300,000 that of Earth
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How do we know the Sun’s Density?
• Divide the Sun’s mass by its Volume
• Volume = 4π × (radius)3
• Conclusion: Since the Sun’s density is so low, it must consist of very light materials
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How do we know the Sun’s Temperature?
• Use the fact that the Sun is a “blackbody” radiator
• It puts out its peak energy in visible light, hence it must be about 6000 K at its surface
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Reminder: Black Body Spectrum• Objects emit radiation of all frequencies,
but with different intensities
Higher Temp.
Lower Temp.Ipeak
Ipeak
Ipeak
fpeak<fpeak <fpeak
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How do we know the Sun’s composition?
• Take a spectrum of the Sun, i.e. let sunlight fall unto a prism
• Map out the dark (Fraunhofer) lines in the spectrum
• Compare with known lines (“fingerprints”) of the chemical elements
• The more pronounced the lines, the more abundant the element
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Spectral Lines – Fingerprints of the Elements
• Can use spectra to identify elements on distant objects!
• Different elements yield different emission spectra
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• The energy of the electron depends on orbit• When an electron jumps from one orbital to another, it
emits (emission line) or absorbs (absorption line) a photon of a certain energy
• The frequency of emitted or absorbed photon is related to its energy
E = h f (h is called Planck’s constant, f is frequency, another word for
color )
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Sun
• Compare Sun’s spectrum (above) to the fingerprints of the “usual suspects” (right)
• Hydrogen: B,FHelium: CSodium: D
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“Sun spectrum” is the sum of many elements – some Earth-based!
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The Sun’s Spectrum
• The Balmer line is very thick lots of Hydrogen on the Sun
• How did Helium get its name?
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How do we know the Sun’s rotation period?
• Crude method: observe sunspots as they travel around the Sun’s globe
• More accurate: measure Doppler shift of spectral lines (blueshifted when coming towards us, redshifted when receding).– THE BIGGER THE SHIFT, THE HIGHER
THE VELOCITY
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How do we know how much energy the Sun produces each second?
• The Sun’s energy spreads out in all directions
• We can measure how much energy we receive on Earth
• At a distance of 1 A.U., each square meter receives 1400 Watts of power (the solar constant)
• Multiply by surface of sphere of radius 149.6 bill. meter (=1 A.U.) to obtain total power output of the Sun
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Energy Output of the Sun• Total power output: 4 1026 Watts• The same as
– 100 billion 1 megaton nuclear bombs per second
– 4 trillion trillion 100 W light bulbs– $10 quintillion (10 billion billion) worth of
energy per second @ 9¢/kWh
• The source of virtually all our energy (fossil fuels, wind, waterfalls, …)– Exceptions: nuclear power, geothermal
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Where does the Energy come from?
• Anaxagoras (500-428 BC): Sun a large hot rock – No, it would cool down too fast
• Combustion?– No, it could last a few thousand years
• 19th Century – gravitational contraction?– No! Even though the lifetime of sun would be
about 100 million years, geological evidence showed that Earth was much older than this
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What process can produce so much power?
• For the longest time we did not know
• Only in the 1930’s had science advanced to the point where we could answer this question
• Needed to develop very advanced physics: quantum mechanics and nuclear physics
• Virtually the only process that can do it is nuclear fusion
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Nuclear Fusion
• Atoms: electrons orbiting nuclei• Chemistry deals only with
electron orbits (electron exchange glues atoms together to from molecules)
• Nuclear power comes from the nucleus
• Nuclei are very small– If electrons would orbit the
statehouse on I-270, the nucleus would be a soccer ball in Gov. Strickland’s office
– Nuclei: made out of protons (el. positive) and neutrons (neutral)
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The Structure of MatterAtom: Nucleus and Electrons
Nucleus: Protons and Neutrons (Nucleons)
Nucleon: 3 Quarks
| 10-10m |
| 10-14m |
|10-15m|
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Nuclear fusion reaction– In essence, 4 hydrogen nuclei combine (fuse) to
form a helium nucleus, plus some byproducts (actually, a total of 6 nuclei are involved)
– Mass of products is less than the original mass– The missing mass is emitted in the form of energy,
according to Einstein’s famous formulas:
E = mc2
(the speed of light is very large, so there is a lot of energy in even a tiny mass)
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Hydrogen fuses to Helium
Start: 4 + 2 protons End: Helium nucleus + neutrinos Hydrogen fuses to Helium