black body radiation physics 113 goderya chapter(s): 7 learning outcomes:
TRANSCRIPT
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Black Body RadiationPhysics 113 Goderya
Chapter(s): 7Learning Outcomes:
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The Amazing Power of Starlight
Just by analyzing the light received from a star, astronomers can retrieve information about a star’s
1. Total energy output
2. Mass
3. Surface temperature
4. Radius
5. Chemical composition
6. Velocity relative to Earth
7. Rotation period
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Temperature Scales
• o F = 9/5(o K) -459.4
• o F = 9/5(o C) + 32
• o K = 273 + o C
o Co K o F
0 32273
100 212373
-100173 -148
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Brightness and Luminosity
• Luminosity (L): The total amount of energy a star radiates in 1 second per square meter.
• Brightness (B): Energy received from the source at different distances.
• Inverse square Law:B ≈ 1/(distance)2
• B = L / 4πR2
• Sun 5 x 1026 watts
4 /12 = 4
4 / 22 = 1
Light rays
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Star as a Black Body
• Black Body Radiator. A hypothetical object that emits Electromagnetic radiation and whose spectrum is continuous with a peak in the wavelength that corresponds to the temperature of the object.
Wavelength
Ene
rgy
Peak wavelength
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Black Body Radiation (1)The light from a star is usually concentrated in a rather narrow range of wavelengths.
The spectrum of a star’s light is approximately a thermal spectrum called a black body spectrum.
A perfect black body emitter would not reflect any radiation. Thus the name “black body”.
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Two Laws of Black Body Radiation
2. The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases. Wien’s displacement law:
max ≈ 3,000,000 nm / TK
(where TK is the temperature in Kelvin).
1. The hotter an object is, the more luminous it is:
L = A**T4
where = Stefan-Boltzmann constant A = surface area;
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Sun’s Temperature• The sun =500
nm
• T = 3 x 10 6/500 = 6000 K
• 10,000 F
• Wein’s Law gives the surface temperature
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Sun’s Luminosity• The sun: T=
6000 K , R=7 x 108 meters. What is its Luminosity?
• L = 4x 3.14 x (7 x 10 8)2 x 6 x 10-8 (6000)4 = 5 x 1026 Watts
• Compare with 40 watts light bulb
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Color and Temperature
Orion
Betelgeuse
Rigel
Stars appear in different colors,
from blue (like Rigel)
via green / yellow (like our sun)
to red (like Betelgeuse).
These colors tell us about the star’s
temperature.
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The Color Index (1)
B bandV band
The color of a star is measured by comparing its brightness in two different wavelength bands:
The blue (B) band and the visual (V) band.
We define B-band and V-band magnitudes just as we did before for total magnitudes (remember: a larger number indicates a fainter star).
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The Color Index (2)
We define the Color Index
B – V(i.e., B magnitude – V magnitude).
The bluer a star appears, the smaller the color index B – V.
The hotter a star is, the smaller its color index B – V.