Download Integrative Studies 410 Our Place in the Universe

Blackbody Radiation & Atomic
Spectra
“Light” – From gamma-rays to radio waves
• The vast majority of information we have about
astronomical objects comes from light they either
emit or reflect
• Here, “light” stands for all sorts of
electromagnetic radiation
• A type of wave, electromagnetic in origin
• Understanding the properties of light allows us to
use it to determine the
– temperature
– chemical composition
– (radial) velocity
of distant objects
Waves
• Light is a type of
wave
• Other common
examples: ocean
waves, sound
• A disturbance in a
medium (water, air,
etc.) that propagates
• Typically the medium
itself does not move
much
crest
Wave Characteristics
wavelength
2 x amplitude
trough
direction of wave motion
• Wave frequency: how often a crest washes over you
• Wave speed = wavelength ()  frequency (f)
Electromagnetic Waves
• Medium = electric and magnetic field
• Speed = 3 105 km/sec
Electromagnetic Spectrum
Energy:
low

medium

high
Electromagnetic Radiation:
Quick Facts
• There are different types of EM radiation, visible
light is just one of them
• EM waves can travel in vacuum, no medium needed
• The speed of EM radiation “c” is the same for all
types and very high ( light travels to the moon in 1
sec.)
• The higher the frequency, the smaller the
wavelength ( f = c)
• The higher the frequency, the higher the energy of
EM radiation (E= h f, where h is a constant)
Visible Light
• Color of light determined
by its wavelength
• White light is a mixture
of all colors
• Can separate individual
colors with a prism
Three Things Light Tells Us
• Temperature
– from black body spectrum
• Chemical composition
– from spectral lines
• Radial velocity
– from Doppler shift
Temperature Scales
Fahrenheit
Centigrade
Kelvin
459 ºF
273 ºC
0K
32 ºF
0 ºC
273 K
Human body
temperature
98.6 ºF
37 ºC
310 K
Water boils
212 ºF
100 ºC
373 K
Absolute zero
Ice melts
Black Body Spectrum
• Objects emit radiation of all frequencies,
but with different intensities
Ipeak
Higher Temp.
Ipeak
Ipeak
Lower Temp.
fpeak<fpeak <fpeak
Cool, invisible galactic gas
(60 K, fpeak in low radio
frequencies)
Dim, young star
(600K, fpeak in infrared)
The Sun’s surface
(6000K, fpeak in visible)
Hot stars in Omega Centauri
(60,000K, fpeak in ultraviolet)
The higher the
temperature of an object,
the higher its Ipeak and fpeak
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Wien’s Law
• The peak of the intensity curve will move
with temperature, this is Wien’s law:
Temperature * wavelength = constant
= 0.0029 K*m
So: the higher the temperature T, the smaller the
wavelength, i.e. the higher the energy of the
electromagnetic wave
Example: Wien’s Law
• Sun T=6000K, Earth t=300K (or you!)
• The Sun is brightest in the visible wave
lengths (500nm). At which wave lengths is the
Earth (or you) brightest?
• Wien: peak wave length is proportional to
temperature itself Scales linearly!
• Factor f=T/t=20, so f1 =201=20, so peak
wavelength is 20x500nm=10,000 nm = 10 um
• Infrared radiation!
Energy & Power Units
• Energy has units Joule (J)
• Rate of energy expended per unit time is called
power, and has units Watt (W)
• Example: a 100 W = 100 J/s light bulb emits 100
J of energy every second
• Nutritional Value: energy your body gets out of
food, measured in Calories = 1000 cal = 4200 J
• Luminosity is the same as power radiated
Stefan’s Law
• A point on the Blackbody curve tells us
how much energy is radiated per frequency
interval
• Question: How much energy is radiated in
total, i.e. how much energy does the body
lose per unit time interval?
• Stefan(-Boltzmann)’s law: total energy
radiated by a body at temperature T per
second: P = A σ T4
• σ = 5.67 x 10-8W/(m2 K4)
Example: Stefan-Boltzmann Law
• Sun T=6000K, Earth t=300K (or you!)
• How much more energy does the Sun
radiate per time per unit area?
• Stefan: Power radiated is proportional to the
temperature (in Kelvin!) to the fourth power
• Scales like the fourth power!
• Factor f=T/t=20, so f4 =204=24x104=16x104
• 160,000 x
Measuring Temperatures
• Find maximal intensity
 Temperature (Wien’s law)
Identify spectral lines
of ionized elements
 Temperature
Color of a radiating blackbody as a
function of temperature
• Think of heating an iron bar in the fire: red
glowing to white to bluish glowing
Spectral Lines – Fingerprints of the Elements
• Can use this to
identify
elements on
distant objects!
• Different
elements yield
different
emission spectra
Kirchhoff’s Laws: Dark Lines
Cool gas absorbs light at specific frequencies
 “the negative fingerprints of the elements”
Kirchhoff’s Laws: Bright lines
Heated Gas emits light at specific frequencies
 “the positive fingerprints of the elements”
Kirchhoff’s Laws
1. A luminous solid or liquid (or a sufficiently dense
gas) emits light of all wavelengths: the black body
spectrum
2. Light of a low density hot gas consists of a series
of discrete bright emission lines: the positive
“fingerprints” of its chemical elements!
3. A cool, thin gas absorbs certain wavelengths from
a continuous spectrum
 dark absorption ( “Fraunhofer”) lines in
continuous spectrum: negative “fingerprints” of its
chemical elements, precisely at the same
wavelengths as emission lines.
Spectral Lines
• Origin of discrete spectral
lines: atomic structure of
matter
• Atoms are made up of
electrons and nuclei
– Nuclei themselves are made up
of protons and neutrons
• Electrons orbit the nuclei, as
planets orbit the sun
• Only certain orbits allowed
Quantum jumps!
• The energy of the electron depends on orbit
• When an electron jumps from one orbital to
another, it emits (emission line) or absorbs
(absorption line) a photon of a certain energy
• The frequency of emitted or absorbed photon is
related to its energy
E=hf
(h is called Planck’s constant, f is frequency)