Kirchhoff’s Laws: Dark Lines

Kirchhoff’s Laws: Dark Lines Cool gas absorbs light at specific frequencies  “the negative fingerprints of the elements”

Kirchhoff’s Laws: Bright lines Heated Gas emits light at specific frequencies  “the positive fingerprints of the elements”

Kirchhoff’s Laws • A luminous solid or liquid (or a sufficiently dense gas) emits light of all wavelengths: the black body spectrum • Light of a low density hot gas consists of a series of discrete bright emission lines: the positive “fingerprints” of its chemical elements! • 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.

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!

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)

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

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)

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

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!

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 ObservatoryVideo

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

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

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

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

Reminder: Black Body Spectrum • Objects emit radiation of all frequencies, but with different intensities Ipeak Higher Temp. Ipeak Ipeak Lower Temp. fpeak<fpeak <fpeak

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

Spectral Lines – Fingerprints of the Elements • Can use spectra to identify elements on distant objects! • Different elements yield different emission spectra

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 )

Sun  • Compare Sun’s spectrum (above) to the fingerprints of the “usual suspects” (right) • Hydrogen: B,FHelium: CSodium: D

“Sun spectrum” is the sum of many elements – some Earth-based!

The Sun’s Spectrum • The Balmer line is very thick  lots of Hydrogen on the Sun • How did Helium get its name?

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

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

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

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

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

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)

Atom:Nucleus and Electrons The Structure of Matter Nucleus: Protons and Neutrons (Nucleons) Nucleon: 3 Quarks | 10-10m | | 10-14m | |10-15m|

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)

Hydrogen fuses to Helium Start: 4 + 2 protons End: Helium nucleus + neutrinos Hydrogen fuses to Helium

Kirchhoff’s Laws: Dark Lines