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ASTR 1200 Announcements Website http://casa.colorado.edu/~wcash/APS1200/APS1200.html HW #1 along back walkway Lecture Notes going up on the website First Exam October 7

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Nature of Light Light is a flux of particles called photons Each photon is both a particle and a wave (a packet of waves) 250 years after Newton we still don’t understand it Electromagnetic Theory (Maxwell’s Equations) 1860’s Quantum Electrodynamics 1948 Feynman Each photon has: direction wavelength polarization

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Light Waves lambda is lower case Greek “L” stands for length Each photon is a sine wave moving at the speed of light Wavelength is usually measure in Angstroms 1Å = 10 -8 cm =10 -10 m about the diameter of an atom. And 10Å = 1 nm Electric and Magnetic Fields Sloshing Back And Forth

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Color Wavelength Determines Color of Light Color is the eye’s response to different wavelengths Color is a physiological effect A photon can have any wavelength RED7000Å YELLOW5500Å VIOLET4000Å

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Electromagnetic Spectrum visible is tiny chunk of em spectrum

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Parts of EM Spectrum Radio > 1mm (10 7 A) Infrared1 mm > > 10000A Visible10,000A > > 3500A Ultraviolet3500A > > 100A X-ray100A > > 0.1A Gamma-ray0.1A >

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Speed of Light Speed of Light is constant c = 3x10 8 m/s That’s a very odd statement 40 km/h 100 km/h

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Speed of Light Speed of Light is constant c = 3x10 8 m/s That’s a very odd statement 60 km/h 40 km/h

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Speed of Light Speed of Light is constant c = 3x10 8 m/s That’s a very odd statement 40 km/h c

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Speed of Light Speed of Light is constant c = 3x10 8 m/s That’s a very odd statement 40 km/h c

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c as a Speed Limit c v = ?? Nothing with mass can reach the speed of light (Everything without mass travels at c)

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Adding Velocities No velocity can exceed the speed of light Have to change how we add velocities

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Time Dilation An observers sees time pass slower in moving objects v See light travel farther All light moves at same speed

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Other Relativistic Effects Length contraction Mass increase Simultaneous Events Explanations in chapter S2

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Frequency Moves during each cycle Frequency is the number of cycles per second, Greek “nu” Moves distance for each of cycles each second Measured in Hertz (Hz) same as 1/s

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Frequency (2) 300MHz = 1m wavelength What’s the wavelength of a 300 MHz photon? c = 3x10 8 m/s; ν = 300 MHz = 3x10 8 Hz

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Question An x-ray has a wavelength of 100Å (10nm, 1x10 -8 m). What is it's frequency, in cycles per second? (aka Hertz) A. 3x10 16 B. 1.5x10 16 C. 3x10 13 D. 1.5x10 13

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Question An x-ray has a wavelength of 100Å (10nm, 1x10 -8 m). What is it's frequency, in cycles per second? (aka Hertz) c = 3x10 8 m/s; λ = 1x10 -8 m A. 3x10 16 Hz

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Light is made of particles called photons For a fixed frequency every photon has the same energy h = 6.63x10 -34 J s Planck’s Constant Energy of a Photon

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How many photons from the sun hit you outside? Yellow photons have frequency ≈ 6x10 14 Hz =(6.6x10 -34 J s)(6x10 14 Hz) = 4x10 -19 J Sunlight is 10 4 W/m 2 (1 W is 1 J/s) (10 4 J/s/m 2 )/(4x10 -19 J/photon) = 2.5x10 22 photons/s/m 2

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Question How many times more energy is there in an x-ray photon at 100A than the infrared light photons emitted by every living human? (Assuming 10,000nm wavelength of infrared light). A. Ten times as powerful. B. A hundred times more powerful. C. A thousand times more powerful. D. 1x10 12 (a trillion) times more powerful. E. 1x10 15 (a quadrillion) times more powerful.

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How many times more energy is there in an x-ray photon at 100A than the infrared light photons emitted by every living human? (Assuming 10,000nm wavelength of infrared light). Question E = hν and ν = c/λ so E = hc/λ First photon has E 1 = hc/λ 1, second has E 2 = hc/λ 2 E 1 hc/λ 1 λ 2 E 2 hc/λ 2 λ 1 __ ____ __ = = E 1 /E 2 = (100,000A)/(100A) = 1000 times brighter

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Electromagnetic Spectrum Wavelength increases to the right Frequency and energy increase to the left

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Spectroscopy Spectrum is plot of number of photons as a function of wavelength Tells us huge amounts about nature of object emitting light.

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Thermal Radiation Planck’s Law Temperature Determines Where Spectrum Peaks Position of Peak Determines Color

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Blue is Hotter than Red Optically Thick, But hot Sunalmost “white hot” Burner“red hot” Desk“black hot” Ice Cube “black hot”

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Question A star with a temperature of 100,000K has what color to the naked eye? a)White b)Yellow c)Orange d)Red

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Question A star with a temperature of 100,000K has what color to the naked eye? a)White b)Yellow c)Orange d)Red

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Wien’s Law As T rises, drops Bluer with temperature Å (T in Kelvin) T 300K100,000AEarth 55005500Sun 10 6 30X-ray source Hotter stars peak at bluer wavelengths

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Question How many times smaller would the peak wavelength be for a star twice as hot as the Sun? (Remember the sun is 5500K) A. Twice as long B. Half as long C. Four times as long D. A fourth as long

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Question How many times smaller would the peak wavelength be for a star twice as hot as the Sun? (Remember the sun is 5500K) λ = (3x10 7 Å K)/T T sun = 5500K T star = 11000K λ star /λ sun = ((3x10 7 Å K)/T star )/ ((3x10 7 Å K)/T sun ) = T sun /T star = 5500K /11000K = 1/2 B. Half as long

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Stefan-Boltzman Law = 5.67x10 -8 W/m 2 /K 4 A is area in m 2 T in Kelvins Example: The Sun L = (5.7x10 -8 W/m 2 /K 4 )x (6.2x10 18 m 2 ) x (5500K) 4 = 4 x 10 26 W 4x10 26 Watts = 100 billion billion MegaWatts!! A = 4πr 2 = 4 x 3.14 x (7x10 8 m) 2 = 6.2x10 18 m 2 L is luminosity in W T = 5500 K Hotter stars emit more energy per area

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Question If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? a)2 b)4 c)8 d)16 e)32

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Question If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? L = σAT 4 A stays the same (radius doesn’t change) T doubles L 2 /L 1 = (σA 2 T 2 4 )/(σA 1 T 1 4 ) = (T 2 /T 1 ) 4 = 2 4 = 16 d.) 16

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Spectral Lines Electrons in atoms have electric potential energy Only specific energies allowed Different for each type of atom

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Emission Lines Electron Drops Photon Escapes Electron drops to lower energy level Emits photon

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Emission Lines

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Absorption Lines Absorbs photon Electron rises to higher energy level Electron rises Photon Absorbed

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Absorption Lines Light moving through cold gas can have photons removed. Creates dark wavelengths called absorption lines

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Example Spectrum

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Question A star is viewed through a far away hydrogen gas cloud, what kind of spectrum can we expect to see? A) Absorption only B) Emission only C) Continuum only D) Emission and Continuum E) Absorption and Continuum

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Question A star is viewed through a far away hydrogen gas cloud, what kind of spectrum can we expect to see? A) Absorption only B) Emission only C) Continuum only D) Emission and Continuum E) Absorption and Continuum

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Stars Come in Different Colors

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Stellar Temperature Stars come in different sizes and temperatures. Can the two be linked?

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Question You see three stars up in the sky. One is bigger than the others and red, one is yellow, and one is white. Which one peaks at a higher frequency? A)Red B)Yellow C)White D)I need to know how far away they are

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Question You see three stars up in the sky. One is bigger than the others and red, one is yellow, and one is white. Which one peaks at a higher frequency? A)Red B)Yellow C)White D)I need to know how far away they are

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Stellar Classification Full range of surface temperatures from 2000 to 40,000K Spectral Classification is Based on Surface Temperature O B A F G K M Oh Be A Fine Gal Guy Kiss Me Each Letter has ten subdivisions from 0 to 9 0 is hottest, 9 is coolest Coolest Hottest { }

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The Spectral Types O Stars of Orion's Belt >30,000 K Lines of ionized helium, weak hydrogen lines <97 nm (ultraviolet)* BRigel 30,000 K- 10,000 K Lines of neutral helium, moderate hydrogen lines 97-290 nm (ultraviolet)* ASirius 10,000 K-7,500 K Very strong hydrogen lines 290-390 nm (violet)* FPolaris 7,500 K- 6,000 K Moderate hydrogen lines, moderate lines of ionized calcium 390-480 nm (blue)* G Sun, Alpha Centauri A 6,000 K- 5,000 K Weak hydrogen lines, strong lines of ionized calcium 480-580 nm (yellow) KArcturus 5,000 K- 3,500 K Lines of neutral and singly ionized metals, some molecules 580-830 nm (red) M Betelgeuse, Proxima Centauri <3,500 K Molecular lines strong >830 nm (infrared) *All stars above 6,000 K look more or less white to the human eye because they emit plenty of radiation at all visible wavelengths.

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Stellar Classification (2) SunG2 CenG2 + K5 SiriusA1 AntaresM1 RigelB8 O540,000K B515,500 A58500 F56580 G55520 K54130 M52800 Letters are odd due to confusion in sorting out temperature scale between 1900 and 1920

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