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ASTR 1020 – February 9 . Second Homework Due Today Planetarium Next Tuesday Feb 14 First Exam Feb 21 Website http://casa.colorado.edu/~wcash/APS1020/APS1020.html 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 Light Waves l 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 = 10-8cm =10-10m about the diameter of an atom. And 10Å = 1nm Electric and Magnetic Fields Sloshing Back And Forth 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 RED YELLOW VIOLET 7000Å 5500Å 4000Å Electromagnetic Spectrum visible is tiny chunk of em spectrum Parts of EM Spectrum Radio Infrared Visible Ultraviolet X-ray Gamma-ray l > 1mm (107A) 1mm> l > 10000A 10,000A > l > 3500A 3500A > l > 100A 100A > l > 0.1A 0.1A > l Question • What range of wavelength can the average human eye see and what color is each side of the spectrum? A) 400nm-800nm, redder to bluer B) 500nm-700nm, bluer to redder C) 400nm-700nm, bluer to redder D) 300nm-600nm, redder to bluer E) None of the above Answer • What range of wavelength can the average human eye see and what color is each side of the spectrum? A) 400nm-800nm, redder to bluer B) 500nm-700nm, bluer to redder C) 400nm-700nm, bluer to redder D) 300nm-600nm, redder to bluer E) None of the above Answer: C Speed of Light Speed of Light c = 3x108m/s That’s a very odd statement 2 cars at 65mph 1 car at 130mph Cover same distance in same amount of time The Relative speeds are the same Relativity .8c .8c Clearly Approaching each other at 1.6c NO!!! v1 v2 v= v1v2 1 2 c per Einstein v= .8c .8c 1.6c = = .975c 2 1 (.8) 1.64 v always less than c if velocities << c, then v=v1+v2 (Concept of time and space changes) Frequency l l l l Moves l during each cycle Frequency is the number of cycles per second, n Moves distance l for each of n cycles each second ln = c Greek “nu” Frequency (2) ln = c 3x108 m / s l= = = 1m 8 n 3x10 Hz c 300MHz = 1m wavelength 3x108 m / s 14 n= = = 6 x 10 Hz 10 l 5000 x10 m c Yellow Light = 600 trillion Hertz Question • An x-ray has a wavelength of 100Å • (10nm, 1x10-8m). What is it's frequency, in cycles per second? (aka Hertz) • A. 3x1016 • B. 1.5x1016 • C. 3x1013 • D. 1.5x1013 Answer • An x-ray has a wavelength of 100Å (10nm, 1x10-8m). What is it's frequency, in cycles per second? (aka Hertz) • A. 3x1016 • B. 1.5x1016 • C. 3x1013 • D. 1.5x1013 • Answer: A. (3E8m/s)/(1E-8m)=3E16 Hz Energy of a Photon = hn h = 6.63x10-34 J s Planck’s Constant = 6.6 x10 34 x6 x1014 = 4 x10 19 J Sunlight is 104 W/m2 energy of yellow photon Outside we have 1023 photons/m2/s hit us 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. 1x1012 (a trillion) times more powerful. • E. 1x1015 (a quadrillion) times more powerful. Answer • 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. 1x1012 (a trillion) times more powerful. • E. 1x1015 (a quadrillion) times more powerful. • Answer: C. 10,000nm/10nm = 1000 Spectroscopy Spectrum is plot of number of photons as a function of wavelength Tells us huge amounts about nature of object emitting light. Thermal Radiation Planck’s Law I= 2hc 2 1 l5 e hc lkT 1 Temperature Determines Where Spectrum Peaks Position of Peak Determines Color Blue is Hotter than Red Optically Thick, But hot Sun almost “white hot” Burner “red hot” Desk “black hot” Ice Cube “black hot” Question A star with a temperature of 100,000K has what color to the naked eye? a) White b) Yellow c) Orange d) Red Wien’s Law l peak 3x10 = T 7 Å (T in Kelvin) As T rises, l drops Bluer with temperature 300K 5500 106 100,000A 5500 30 Earth Sun X-ray source 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 Answer • 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 • Answer: B. Since peak wavelength is a function of the inverse of temperature, doubling the temp of a star would cause it's peak wavelength to cut in half. Stefan-Boltzman Law L = AT 4 = 5.67x108 W/m2/K4 A is area in m2 T in Kelvins Example: The Sun L = 5.7x10-8 x 4 x 3.14 x (7x108m)2 x (5500K)4 = 4 x 1026 W 4x1026 Watts = 100 billion billion MegaWatts!! 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 Answer 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 = 24 e) 32 Emission Lines Electron Drops Enrgy Lvl of H Photon Escapes Can Only Happen Between Certain Pre-determined orbitals Each Element Has Different Orbitals So Each Element Has Different Lines Spectrum of Hydrogen Absorption Lines Light moving through cold gas can have photons removed. Creates dark wavelengths called absorption lines 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 Answer 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 Stars Come in Different Colors Stellar Temperature Stars come in different sizes and temperatures. Can the two be linked? 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 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 Stellar Classification Full range of surface temperatures from 2000 to 40,000K Spectral Classification is Based on Surface Temperature Hottest O B A Oh Be A Fine F G K M Gal Guy { } Kiss Me Each Letter has ten subdivisions from 0 to 9 0 is hottest, 9 is coolest Coolest The Spectral Types Stars of Orion's Belt >30,000 K Lines of ionized helium, weak hydrogen lines <97 nm (ultraviolet)* B Rigel 30,000 K10,000 K Lines of neutral helium, moderate hydrogen lines 97-290 nm (ultraviolet)* A Sirius 10,000 K-7,500 K Very strong hydrogen lines 290-390 nm (violet)* F Polaris 7,500 K6,000 K Moderate hydrogen lines, moderate lines of ionized calcium 390-480 nm (blue)* G Sun, Alpha Centauri A 6,000 K5,000 K Weak hydrogen lines, strong lines of ionized calcium 480-580 nm (yellow) K Arcturus 5,000 K3,500 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) O *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. Stellar Classification (2) Sun a Cen Sirius Antares Rigel G2 G2 + K5 A1 M1 B8 O5 B5 A5 F5 G5 K5 M5 40,000K 15,500 8500 6580 5520 4130 2800 Letters are odd due to confusion in sorting out temperature scale between 1900 and 1920 The Doppler Shift Another Powerful Tool Frequency of light changes depending on velocity of source. Similar to sound wave effect Higher pitch when vehicle approaches Lower when it recedes. Spectral Shifts Spectrum is identifiable as known element, but lines appear shifted. Measure the shift, and we get velocity information! Shift to blueward implies approach Shift to redward implies departure The Doppler Shift vt ct Observer D During t seconds, source emits n waves of wavelength l. They move ct during that time. But source also moves vt during that time. So the n waves are scrunched into ct-vt instead of the usual ct Thus the wavelength is reduced from l to ct vt cv l =l = l 1 v c ct c The Doppler Formula v c l = l0 1 l l0 l V = = l0 l0 c v is positive if coming toward us Wavelength l decreases from lab value n v v0 V = = n0 v0 c Frequency shifts up as source approaches Doppler Examples I run toward you with laser at 3m/s c = 3x108m/s, l = 6328Å v/c = 10-8 So l = l x v/c = 6328 x 10-8 = 6.3x10-5 l = 6328.000063Å ---- That’s why we can’t sense a change Shuttle orbits at 6km/s v/c = 6/300,000 = 2x10-5 100MHz becomes 100MHz + 108 x 2x10-5 = 100,002,000Hz if coming at you. Another Doppler Example Star has known hydrogen line at 6563Å Detect line at 6963Å l = 400Å l 400 v=c = 300,000 = 18,284km / s l0 6563 Star is receding at 18,000km/s !! In some cases astronomers can detect shifts as small as one part in a million. That implies detection of motion as small as 300m/s. What about that #@&! radar gun? Cop uses radar which typically operates near l = 1cm If you are going 65mph = 65 mi/hr x 1600m/mi / (3600 s/hr) = 30m/s This creates a shift of l = 30/3x108 = 10-7 in the wavelength 1cm shifts to .9999999 cm. Not much. To say you were 5mph over the limit needs to measure one part in 100million! Example of How Its Used in Astronomy Stellar lines are broadened by star’s rotation. Stellar Luminosity By 1915 had lots of spectra and classifications Had a few distances from parallax Once distance was available, luminosity and Absolute Magnitude could be calculated. Herzsprung and Russel, working independently both plotted absolute magnitude (luminosity) vs classification (temperature) The H-R Diagram Plot of Brightness vs Temperature -5 Giants Rigel Capella Brightness 0 Sirius Procyon Sun +5 Main Sequence a Cen B White Dwarfs +10 Sirius B Prox Cen +15 O B A F G Spectral Type K M The H-R Diagram The Main Sequence Stars Differ By: Mass Age Composition Nothing else! And composition doesn’t vary Age and Mass only. Those on main sequence are all burning H so age drops out. MS is function of MASS only!!! Full, Artistic H-R As mass of MS star increases, both R and T increase increasing size AT4 T constant on any vertical line Newly Formed Star -5 Giants Rigel Capella 0 M Sirius Protostar Procyon Sun +5 Main Sequence Then sits while burning H a Cen B White Dwarfs +10 Sirius B Prox Cen +15 O B A F G Spectral Type K Large, Low T. Settles down to MS M MS Lifetime What determines amount of time a star stays on Main Sequence? Just like a kerosene heater: Amount of fuel and rate of burn. More Mass = More Fuel More Luminosity = Greater Burn Rate We can scale from the Sun: M = 1M L = 1L Sun lasts 1010 years M MSLife = 10 L 10 M in solar masses L in solar luminosities Some Lifetimes Sun Sirius Prox Cen Rigel Mass Luminosity Lifetime in Billion Years 1 2 .4 8 1 10 .001 10,000 10 2 4000 .008 Dinky little stars like Prox Cen will last trillions of years Huge stars like Rigel are gone in a few million There aren’t many large stars out there, because they don’t last. 10,000 O stars of the 100,000,000,000 Milky Way stars