Download Lecture 8

ASTR 1200
Announcements
HW #1 along back walkway
Lecture Notes going up on the website
First Exam October 7
Website
http://casa.colorado.edu/~wcash/APS1200/APS1200.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
Speed of Light
Speed of Light is constant
c = 3x108m/s
That’s a very odd statement
100 km/h
40 km/h
Speed of Light
Speed of Light is constant
c = 3x108m/s
That’s a very odd statement
60 km/h
40 km/h
Speed of Light
Speed of Light is constant
c = 3x108m/s
That’s a very odd statement
40 km/h
c
Speed of Light
Speed of Light is constant
c = 3x108m/s
That’s a very odd statement
40 km/h
c
c as a Speed Limit
• Nothing with mass can reach the speed of
light
• (Everything without mass travels at c)
v = ??
c
Adding Velocities
• No velocity can exceed the speed of light
• Have to change how we add velocities
v1  v2
v
v1v2
1 2
c
Time Dilation
• An observers sees time pass slower in
moving objects
See light travel farther
All light moves at same
speed
v
Other Relativistic Effects
• Length contraction
• Mass increase
• Simultaneous Events
Explanations in chapter S2
Frequency
l
l
l
l
Moves l during each cycle
Frequency is the number of cycles per second,
n
Measured in Hertz (Hz) same as 1/s
Moves distance l for each of n cycles each second
ln  c
Greek “nu”
Frequency (2)
What’s the wavelength of a 300 MHz photon?
ln  c
c
λ
ν
c = 3x108 m/s; ν = 300 MHz = 3x108 Hz
c 3x108 m / s
λ 
 1m
8
ν 3x10 Hz
300MHz = 1m wavelength
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
Question
• An x-ray has a wavelength of 100Å
(10nm, 1x10-8m). What is it's frequency, in
cycles per second? (aka Hertz)
c
ν
λ
c = 3x108 m/s; λ = 1x10-8m
c 3x108 m / s
16
ν 

3
x
10
Hz

8
λ 1x10 m
A. 3x1016 Hz
Energy of a Photon
• Light is made of particles called photons
• For a fixed frequency every photon has
the same energy
•   hn
• h = 6.63x10-34 J s Planck’s Constant
Energy of a Photon
How many photons from the sun hit you outside?
Yellow photons have frequency ≈ 6x1014 Hz
ε  hν
=(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
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.
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 = hν and ν = c/λ so E = hc/λ
First photon has E1 = hc/λ1, second has E2 = hc/λ2
E
hc/λ1 __
λ2
__1 ____
=
=
E2 hc/λ2 λ1
E1/E2 = (100,000A)/(100A) = 1000 times brighter
Electromagnetic Spectrum
• Wavelength increases to the right
• Frequency and energy increase to the left
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
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
Hotter stars peak at bluer wavelengths
l peak
3x10

T
7
Å
(T in Kelvin)
As T rises, l drops
Bluer with temperature
T
300K
5500
106
l
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
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 = (3x107 Å K)/T
Tsun = 5500K
Tstar = 11000K
λstar/λsun = ((3x107 Å K)/Tstar)/ ((3x107 Å K)/Tsun)
= Tsun /Tstar
= 5500K /11000K = 1/2
B. Half as long
Stefan-Boltzman Law
Hotter stars emit more energy per area
L  AT
4
 = 5.67x10-8 W/m2/K4
A is area in m2
T in Kelvins
L is luminosity in W
Example: The Sun
A = 4πr2 = 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!!
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
Question
If you were to double the temperature of the
Sun without changing its radius, by what
factor would its luminosity rise?
L = σAT4
A stays the same (radius doesn’t change)
T doubles
L2/L1 = (σA2T24)/(σA1T14) = (T2/T1)4
d.) 16
4
= 2 = 16
Spectral Lines
• Electrons in atoms
have electric
potential energy
• Only specific
energies allowed
• Different for each
type of atom
Emission Lines
• Electron drops to
lower energy level
• Emits photon
Electron Drops
Photon Escapes
Emission Lines
Absorption Lines
• Absorbs photon
• Electron rises to higher
energy level
Electron rises
Photon Absorbed
Absorption Lines
Light moving through cold
gas can have photons removed.
Creates dark wavelengths
called absorption lines
Example Spectrum
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
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
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
F
G
K
Gal
Kiss Me
Guy
{ }
Oh Be A Fine
Each Letter has ten subdivisions from 0 to 9
0 is hottest, 9 is coolest
M
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