ASTR 1040 – September 21 Second Homework Due next Thursday 28th Planetarium Next Tuesday September 26 First Exam October 5 Observatory Opportunity Next Tuesday 26th Website http://casa.colorado.edu/~wcash/APS1040/APS1040.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 RED 7000Å YELLOW 5500Å VIOLET 4000Å 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 7000Å YELLOW 5500Å VIOLET 4000Å

Electromagnetic Spectrum visible is tiny chunk of em spectrum

Parts of EM Spectrum Radio l > 1mm (107A) Infrared 1mm> l > 10000A Visible 10,000A > l > 3500A Ultraviolet 3500A > l > 100A X-ray 100A > l > 0.1A Gamma-ray 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 NO!!! .8c .8c Clearly Approaching each other at 1.6c v always less than c if velocities << c, then v=v1+v2 per Einstein (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 Greek “nu” Moves distance l for each of n cycles each second

Frequency (2) 300MHz = 1m wavelength 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 h = 6.63x10-34 J s Planck’s Constant energy of yellow photon Sunlight is 104 W/m2 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 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? White Yellow Orange Red

Wien’s Law Å As T rises, l drops Bluer with temperature (T in Kelvin) 300K 100,000A Earth 5500 5500 Sun 106 30 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 s = 5.67x10-8 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? 2 4 8 16 32

Answer If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? 2 4 8 16 = 24 32

Emission Lines Electron Drops Energy Levels of H Photon Escapes Can Only Happen Between Certain Pre-determined orbitals Spectrum of Hydrogen Each Element Has Different Orbitals So Each Element Has Different Lines

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?