Transcript Wednesday, April 9

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
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.
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=hf
(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
Solar Dynamics Observatory Video
elements
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=hf
(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,F
Helium: C
Sodium: 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=
2
mc
(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