ASTR 1200 Announcements

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ASTR 1200Announcements
HW 1 along back walkway Lecture Notes going up
on the website First Exam October 7
Website http//casa.colorado.edu/wcash/APS1200/AP
S1200.html
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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 dont
understand it Electromagnetic Theory (Maxwells
Equations) 1860s 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
10-8cm 10-10m about the diameter of an
atom. And 10Å 1nm
Electric and Magnetic Fields Sloshing Back And
Forth
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Color
Wavelength Determines Color of Light Color is
the eyes response to different
wavelengths Color is a physiological effect A
photon can have any wavelength
RED 7000Å YELLOW 5500Å VIOLET 4000Å
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Electromagnetic Spectrum
visible is tiny chunk of em spectrum
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Parts of EM Spectrum
Radio l gt 1mm (107A) Infrared 1mmgt l gt
10000A Visible 10,000A gt l gt 3500A Ultraviolet 3
500A gt l gt 100A X-ray 100A gt l gt
0.1A Gamma-ray 0.1A gt l
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Speed of Light
Speed of Light is constant c 3x108m/s
Thats a very odd statement
100 km/h
40 km/h
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Speed of Light
Speed of Light is constant c 3x108m/s
Thats a very odd statement
60 km/h
40 km/h
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Speed of Light
Speed of Light is constant c 3x108m/s
Thats a very odd statement
40 km/h
c
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Speed of Light
Speed of Light is constant c 3x108m/s
Thats a very odd statement
c
40 km/h
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c as a Speed Limit

• Nothing with mass can reach the speed of light
• (Everything without mass travels at c)

v ??
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

See light travel farther
All light moves at same speed
v
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Other Relativistic Effects

• Length contraction
• Mass increase
• Simultaneous Events
• Explanations in chapter S2

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Frequency
Moves l during each cycle
Frequency is the number of cycles per second, n
Greek nu
Measured in Hertz (Hz) same as 1/s
Moves distance l for each of n cycles each second
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Frequency (2)
Whats the wavelength of a 300 MHz photon?
c 3x108 m/s ? 300 MHz 3x108 Hz
300MHz 1m wavelength
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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

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Question

• An x-ray has a wavelength of 100Å(10nm,
  1x10-8m). What is it's frequency, in cycles per
  second? (aka Hertz)

c 3x108 m/s ? 1x10-8m
A. 3x1016 Hz
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Energy of a Photon

• Light is made of particles called photons
• For a fixed frequency every photon has the same
  energy
• h 6.63x10-34 J s Plancks Constant

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Energy of a Photon

• How many photons from the sun hit you outside?

Yellow photons have frequency 6x1014 Hz
(6.6x10-34 J s)(6x1014 Hz) 4x10-19 J
Sunlight is 104 W/m2 (1 W is 1 J/s)
(104 J/s/m2)/(4x10-19 J/photon) 2.5x1022
photons/s/m2
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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. 1x1012 (a trillion) times more powerful.
• E. 1x1015 (a quadrillion) times more powerful.

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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).

E h? and ? c/? so E hc/?
First photon has E1 hc/?1, second has E2 hc/?2
E1/E2 (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
Plancks Law
Temperature Determines Where Spectrum Peaks
Position of Peak Determines Color
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Blue is Hotter than Red
Optically Thick, But hot Sun almost 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?
• White
• Yellow
• Orange
• Red

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Question

• A star with a temperature of 100,000K has what
  color to the naked eye?
• White
• Yellow
• Orange
• Red

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Wiens Law
Hotter stars peak at bluer wavelengths
Å
(T in Kelvin)
As T rises, l drops Bluer with temperature
T l 300K 100,000A Earth 5500 55
00 Sun 106 30 X-ray source
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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)

? (3x107 Å K)/T
Tsun 5500K Tstar 11000K
?star/?sun ((3x107 Å K)/Tstar)/ ((3x107 Å
K)/Tsun)
Tsun /Tstar
5500K /11000K 1/2
B. Half as long
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Stefan-Boltzman Law
Hotter stars emit more energy per area
s 5.67x10-8 W/m2/K4
A is area in m2
T in Kelvins
L is luminosity in W
Example The Sun
A 4pr2 4 x 3.14 x (7x108 m)2 6.2x1018 m2
T 5500 K
L (5.7x10-8 W/m2/K4 )x (6.2x1018 m2) x (5500K)4
4 x 1026 W
4x1026 Watts 100 billion billion MegaWatts!!
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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?
• 2
• 4
• 8
• 16
• 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 sAT4
A stays the same (radius doesnt change) T doubles
L2/L1 (sA2T24)/(sA1T14) (T2/T1)4
d.) 16
24 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 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

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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 onlyD) Emission
  and ContinuumE) 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 onlyD) Emission
  and ContinuumE) 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
Coolest
Hottest


Gal
Kiss Me
Oh Be A Fine
Guy
Each Letter has ten subdivisions from 0 to 9 0 is
hottest, 9 is coolest
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The Spectral Types
O Stars of Orion's Belt gt30,000 K Lines of ionized helium, weak hydrogen lines lt97 nm (ultraviolet)
B Rigel 30,000 K-10,000 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 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)
K Arcturus 5,000 K-3,500 K Lines of neutral and singly ionized metals, some molecules 580-830 nm (red)
M Betelgeuse, Proxima Centauri lt3,500 K Molecular lines strong gt830 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. 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. 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. 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)
Sun G2 a Cen G2 K5 Sirius A1 Antares M1 Rigel
B8
O5 40,000K B5 15,500 A5 8500 F5 6580 G5 5520 K5 41
30 M5 2800
Letters are odd due to confusion in sorting out
temperature scale between 1900 and 1920