Transcript Integrative Studies 410 Our Place in the Universe

Atomic Spectra & Doppler Shift
Demos for Optics from last time
• Optical Board
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Lens & mirror
Kepler & Galileo Telescope (inverts/does not)
Eye: normal, near, far sighted
Prism: different color (red/green)  different
angle
iSkylab Stage 2
• How to estimate the period of the “second”
motion (seasonal or montly)
– Sun: we are measuring the decrease of altitude
per day. Expect: 4 x 23.5 deg = 97 deg
• Example: you measured 0.5 deg/ day = 365*0.5
deg/year
– Moon: either same as sun, or, if you measured
motion with respect to stars, e.g. 10 deg/ day =
300 deg/month
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)
Demonstration
• Gas Lamps
• Which one is He, which is H?
• Combined, you are looking at 99% of the
(non-dark) matter content of the universe!
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
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!
Homework Questions
• Boltzmann: Scaling: area = R^2, T^4
Activity: Black Body Radiation
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Pick up a worksheet
Form a group of 3-4 people
Work on the questions on the sheet
Fill out the sheet and put your name on top
Hold on to the sheet until we’ve talked about
the correct answers
• Hand them in at the end of the lecture or during
the break
• I’ll come around to help out !
Doppler Shift
• From Wikipedia
Doppler Shift
• Can use the Doppler shift to
determine radial velocity of
distant objects relative to us
• Transverse velocity can be
measured from the motion of
stars with respect to background over a period of years
– (Halley 1718: Sirius, Arcturus, Aldebaran
moved since Hipparchus, 1850 years ago)
Not Used
Homework: Doppler Shift of
Hydrogen spectrum
• The discrepancy between the wavelength of
a line measured in the lab versus measured
on an object is proportional to the velocity
of the object
• Apparent/ true wavelength = 1+ velocity/c
• Example:
– Observed(or apparent): 698 nm
– Actual(or true or lab) wavelength: 656.3nm
– velocity = (698nm/656.3nm -1) c = 19100 km/s
Group Activity: Estimate Power
• Estimate how much energy you radiate per
second
• Estimate how many candy bars you would
have to eat per day to be able to do that
• Ponder the paradox
Doppler Shift and Stellar
Magnitudes