Download The Fingerprints of Atoms

Reminders!
Website: http://starsarestellar.blogspot.com/ Lectures 1
and 2 are available for download as study aids.
Email: If you have not received an email from me, send
me an email to make sure I can contact you
[email protected]
Reading: Be sure to keep up. You should have at least
pages 1-27 by now. I suggest you read pages 28-37 and
chapter 3 by the end of the weekend.
Homework: Save the chapter 4 problems for the next
homework set. Just do the chapters 1, 2, and 3
problems on homework #1. Remember, this is due next
Wednesday at the BEGINNING of class.
Research Paper
Astronomy is really in a golden age. The number of large
telescopes covering almost every wavelength mean that exciting
discoveries are being reported every day. The goal is to get you to
read and learn about new results in the world of astronomy.
• Due Monday, June 22nd at the beginning of class. It will not be
accepted late!
• Should be THREE, typed pages long. One side per page.
• Additional pages are allowed for the bibliography and any figures.
• You must have at least THREE references. Include a reference
for the book or magazine, or the URL and webpage title if it is a
website.
• You may use Wikipedia to help you get started, but Wikipedia
CANNOT be one of your references!
• Do not plagiarize! Everything must be in your own words!
Research Paper Topics
1. Gamma-ray bursts: Some of the most energetic explosions in
the Universe? What are they?
2. Astronomy and Civilizations: Research THREE different ways
in which astronomy has affected civilizations.
3. The Year of Astronomy: Discuss how astronomers can do a
better job of getting the public excited about astronomy.
4. Is Pluto a Planet?: Discuss the recent decision to make Pluto a
dwarf planet instead of a planet.
5. The Mysterious Dark Matter: 90% of the mass in the Universe
is made of some mysterious matter that we don’t know. What could
it be?
6. Heaven and Earth Collide: Is the Earth in danger of being hit by
a meteor? What can we do to save ourselves?
The Fingerprints of Atoms
Today’s Lecture:
• Review yesterday’s lecture
Wavelength, frequency, and the speed of light
The relation between color and temperature
• How do we know what stars are made of?
Atomic energy levels
The spectra of stars
• The Doppler effect
Wavelength, Frequency, and Speed
λν = v = c, the speed of light!
Since c is a constant, λ and ν are inversely proportional!
The Electromagnetic Spectrum
• γ (gamma) rays:
l < 0.1 Å
• X-rays:
~0.1 - 100 Å
• Ultraviolet (UV):
~100 - 4000 Å
• Visible (optical):
~4000 - 7000 Å
• Infrared (IR):
~7000 Å - 1 mm
• Radio:
~1 mm - 10 km and more
There is NO qualitative difference between different
types of electromagnetic waves. They have different
frequencies and wavelengths, but the SAME speed, c
(independent of the observer or source’s speed).
But the the detection techniques can vary greatly!
What composes a star’s spectrum?
Stars are huge, opaque, luminous balls of gas held
together by gravity.
• Very hot inner parts
emit continuous
radiation. This gives
the spectrum it’s
shape.
• Cooler outer layers
absorb certain
wavelengths, creating
absorption lines.
From this we derive the
chemical composition.
Hotter objects emit
shorter λ
Cooler objects emit
longer λ
T(K)
λpeak (Å)
3500
4000
4500
5000
5500
8300
7300
6400
5800
5300
Wien’s Law
λpeakT = constant
≈ 2.9 x 107 Å K
Stefan-Boltzmann Law
The Stefan-Boltzmann Law tells you how much energy
per unit area is emitted from a black body.
ε = σ T4 (σ = Greek letter “sigma” = constant)
Energy per area per sec
Because of the T4 power, hotter
object emit MUCH more energy per
area than cold objects.
Example:
6000 K
3000 K
If a star is 2x as hot, it emits 16
times more power! (if the two stars
have the same surface area)
Luminosity (or Power)
This is the amount of energy emitted per second by the
entire object.
For a sphere of radius R, Surface Area = 4πR2, so that
If we know both L and T, then we can derive the radius, R!
Revisiting Orion
The stars Betelgeuse and
Rigel have about the same
brightness and about the
same distance, but are very
different colors.
What must be different
between Betelgeuse and
Rigel ?
Revisiting Orion
The radius (and thus surface area) of Betelgeuse must be
larger to output the same power as Rigel!
In fact, Betelgeuse is 1000x the size of the Sun, while Rigel
is merely 62x the size of the Sun. Both have luminosities
that are ~100,000x that of the sun!
What composes a star’s spectrum?
Stars are huge, opaque, luminous balls of gas held
together by gravity.
• Very hot inner parts
emit continuous
radiation. This gives
the spectrum it’s
shape.
• Cooler outer layers
absorb certain
wavelengths, creating
absorption lines.
From this we derive the
chemical composition.
Atoms!
10-8 cm
• The size of a proton or neutron is ~10-13 cm. The mass of
an electron is 1/1830 of the proton or neutron.
• The electron can only “orbit” in discrete energy levels.
Electrons have discrete energy levels
Hydrogen (H) in the
ground state (the
lowest energy
configuration)
+
1
2 3
Outer levels (or “orbits”) have a greater amount of energy
than the inner levels (or “orbits”).
4
Absorbing a photon moves the electron to a
higher energy level (or “orbit”).
Hydrogen
(ground state)
+
1
Photon with
E = hν
Hydrogen
(exited state)
+
3
Before
absorption
+
2
Ephoton = ΔE = E4 - E2 = hνphoton
(difference in energy levels)
After
absorption
+
4
+
The electron almost
instantly jumps back
down to a lower
energy level.
When this happens,
it emits a photon.
• Emission occurs in a random direction.
• Several jumps can occur until the atom comes to the
lowest energy level.
“Absorption Line”
brightness
Some green photons are now missing at a very specific
energy level.
V
I
B
G
Y
O
R
λ
The Hydrogen Spectrum
Lyman
δ
ε
α
Balmer
β
γ
γ
δ
β
α
+
α
β
γ
Paschen
• You don’t need to
remember this in detail.
Just know that bigger
electron jumps
correspond to higher
energy photons.
• Each element
produces an unique
series of lines that acts
like a “fingerprint”
• This allows us to
identify elements in the
Universe that cannot be
measured directly.
The Sun’s spectrum
• Often called a Fraunhofer spectrum, after the scientist
Joseph Fraunhofer (1800s)
• Mainly dominated by Hydrogen, Calcium, and Iron
• In fact, Helium was first discovered by looking at the
spectrum of the Sun. Helium is named after the Greek God
for the Sun, Helios.
Emission Spectrum
• An absorption spectrum is
made from a cold, absorbing
layer on top of a hot, thermal
emitter.
• But remember, the absorption
isn’t absolute. What really
happens is that atoms absorb
the light and then re-emit in all
other directions.
• This means that in other
directions there’s actually
ADDITIONAL emission.
• This gives rise to an
“emission spectrum.”
+
The Doppler Effect
• Enormously important tool
• Used to determine the radial velocity (the speed toward or
away from us)
Stationary emitter
of waves, λ0
Wave crests equally
spaced in all directions
The Doppler Effect
Moving emitter
of waves
• Waves are spaced
closer in the direction
of motion
• Waves are further
apart in the opposite
direction.
Blueshifted
photons
Redshifted
photons
The Doppler Shift of Spectral Lines
Hβ
Hα
Brightness
Hγ
Brightness
Brightness
4341Å 4861Å
6563Å
Hydrogen Balmer lines
with NO SHIFT (v=0)
λ
Redshifted lines
(v is away from us)
λ
Blueshifted lines
(v is toward us)
λ
Radial Motion of Stars
λ0 = rest frame wavelength
Δλ = change in wavelength
due to the Doppler shift
Example: A line that is usually at λ0 = 6563Å is instead
seen at λ = 6565Å. What is the object’s speed?
Δλ = 2Å, so that Δλ/λ0 = 2/6563 = 3 x 10-4
Using the above formula, v/c = 3 x 10-4.
V = (3 x 10-4)c = (3 x 10-4)(3 x 105 km/s) = 90 km/s. Since
the wavelength has increased, the object is moving away
from us (it’s redshifted).