Exam #3 Final Exambogner/isp209s2010/lectures/...ISP209s10 Exam3 Review -1-Exam #3 •Exam #3 is...
Transcript of Exam #3 Final Exambogner/isp209s2010/lectures/...ISP209s10 Exam3 Review -1-Exam #3 •Exam #3 is...
ISP209s10 Exam3 Review -1-
Exam #3
• Exam #3 is Thursday 4/29 in this room
• You can bring 2 page of notes (front and back)
• Bring your calculator and a #2 pencil
• Exam 3 covers material from 4/1 onward
(only 8 lectures)
• Consequently, no extra credit for Exam 3
NOTE: Last HW (# 11) due Friday 4/30 at 8am
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Final Exam
• The Final Exam is on LON-CAPA.
• Opens 4/29 at 4pm and is due Monday 5/3 at 4 pm.
• I don’t care if you work together and/or use your
notes.
• Consequently, no extra credit for the Final.
• Pay close attention to the # of tries you are given for
each problem. Some will only have 1 try, whereas
others will have more.
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Exam 3 review
• A detailed outline of study topics is here:
http://www.nscl.msu.edu/~bogner/isp209s2010/review3.htm
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How do we measure properties of a star?
How do we know what our
sun (and other stars) are made
of ?
How do we know the
temperature?
How do we know the size?
From the spectrum of the EM radiation
from the star (“Blackbody radiation”)
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Some Clicker Questions - #1
What happens to a star if its surface temperature is increased and
its size remains the same?
A) It only gets brighter
B) It only gets more red
C) It gets brighter and more blue
D) It only gets dimmer
E) It gets dimmer and more red
Hint: recall how color correlates with temperature
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Some Clicker Questions - #1
What happens to a star if its surface temperature is increased and
its size remains the same?
A) It only gets brighter
B) It only gets more red
C) It gets brighter and more blue
D) It only gets dimmer
E) It gets dimmer and more red
Remember the correlation between color and
Temperature Blue: Hotter Red: Colder
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Hertzsprung-Russell Diagram:How a star evolves
Luminosity
vs.
Temperature
Observed stars tend
to fall on various
“branches” in this
plot.
Which “branch” a star
Falls on depends on
How it generates its
Energy (I.e., what
Fusion chains occur) ISP209s10 Exam3 Review -8-
A Sample Problem
• Suppose star A and star B have the same luminosity.
• If star A is 5 times brighter than star B, what can we
say about their relative distances?
• Star B is farther away
ab
a
b
b
b
a
a
b
a ddd
d
d
L
d
L
b
b
d
Lbrightness
!="===
==
55
4
4
4(distance)4
luminosity
2
2
2
2
22
#
#
##
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Some Other Star Things …
• Know what powers stars (nuclear fusion reactions)
• Know the 4 steps in how a star is born
• Know that the most important variable that
controls a star’s features is its mass.
• Be familiar with the timeline evolution of our own
sun.
• Understand what we mean when we say “we are
star stuff”.
ISP209s10 Exam3 Review -10-
How did the Universe Begin?
• Evidence points to the Universe beginning in a hot
fireball 13.7 billion years ago. We call this the Big
Bang
• Evidence for the Big Bang
– Expansion of the Universe
– The Big Bang model correctly predicts the formation of
the light elements observed to be present in the early
universe (mostly hydrogen and helium).
– The cosmic microwave background radiation
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Hubble Expansion
• Hubble observed that on average all galaxies seemto be moving away from us.
• The speed is related to distance. Galaxies fartheraway are moving faster
• Hubble Law:
• If a galaxy is observed to be moving away at 2000km/s, we expect the galaxy is v/H0=100 Mly away
Mly
skm /20H distance;Hvelocity 00 =!=
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Big Bang Timeline (the early moments)
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Inflation
Years since the Big Bang
Met
ers
The existence of
an unknown
scalar field
caused the rapid
inflation of the
Universe
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Why does time always move in one direction?
• Inflation during the Big Bang resulted in auniverse that had a very low entropy. Much toolow for its size.
• Hence, everything in the Universe moves towardreaching the correct amount of entropy.
• Time has a direction because going back in timewould imply the entropy could be decreased.
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Clicker Question
• Which of the following events occurred earliest
in the Big Bang? Choose the best answer.
A. hydrogen and helium were made
B. the era of inflation where universe grew by
1050 times
C. electrons combined with nuclei
D. galaxies formed
E. stars formed
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What is the Ultimate Fate
• 10100 years – all the stars will have usedtheir fuel
• 10100 to 10150 years “dark ages”
• 10150 years all black holes will haveevaporated
• 101000 years the Universe will reach itslowest energy state
• Note: The current age of the Universe is13.7 billion years 1010 years
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Other Big Bang Stuff…
• Understand why the CMB radiation map is like
looking at a baby picture of the universe “only”
379,000 years after the Big Bang
• Know why the splotchiness in the CMB is
important to be consistent observed features of the
universe
• Know the expansion of the universe is an
expansion of space itself
• Know how the evidence for the Big Bang was
discovered by accidentISP209s10 Exam3 Review -18-
Some Clicker Questions - #1
The lightest two elements in nature are hydrogen and helium.
Where do we think most atoms of other elements made?
A) In the Big Bang
B) In Stars
C) On planets
D) In space between stars
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Some Clicker Questions - #2
In the Big Bang, what was the inflationary epoch
A) It was the start of the Big Bang
B) It was the period when the Universe increased in size by
1050
C) It was the period when nuclei were made
D) It was the period when atoms where made
ISP209s10 Exam3 Review -20-
Some Clicker Questions - #3
What do we think caused the Big Bang?
A) A Big Crunch
B) Gravity
C) A large explosion
D) The weak force and many neutrinos
E) We don’t know
(NOTE: There are some speculations in String Theory as to
A possible cause)
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Some Clicker Questions - #4
What will happen in the future?
A) We will have a Big Crunch
B) We think the Universe will expand forever
C) We think the Universe will stop expanding and be stationary in
about 10 billion years
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Clicker Question
What is our best guess on the current age of the
Universe, and when will all the stars have burned
out?
A). 13.7 billion years, 10100 billion years
B). 137 billion years, 1010 billion years
C). 13.7 billion years, 1010 billion years
D). 1370 billion years, 101000 billion years,
E). 1.37 billion years, 1010 billion years
ISP209s10 Exam3 Review -23-
Escape Velocity
Earth
v
The velocity to completely escape the
gravity of a planet is:
planet
planet
R
GMv
2=
Something interesting happens (black hole) when v = c.
Mass, m
ISP209s10 Exam3 Review -24-
Clicker Question
What would happen to the escape velocity of
a planet if the radius of the planet were 2
times larger and the mass was the same?
A.It would be !2 times larger
B.It would be !2 times smaller
C.It would be 2 times larger
D.It would be 2 times smaller
planet
planet
R
GMv
2=
ISP209s10 Exam3 Review -25-
Clicker Question
What would happen to the escape velocity of
a planet if the mass of the planet were 4 times
larger and the radius was the same?
A.It would be !2 times larger
B.It would be !2 times smaller
C.It would be 2 times larger
D.It would be 2 times smaller
planet
planet
R
GMv
2=
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Black Holes
The “hole” in space is so deep that
light can not escape.
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Black Holes
• Black holes act as a lens. They don’t necessarily look“black”.
• They range from 3 solar masses to more than a billion solarmasses.– Small ones are formed by the collapse of a large star
– Larger ones form at the center of galaxies
– Typical event horizon for a black hole with the mass of our Sun is15 km
• We can tell they exist because of thing orbiting nothing,and the radiation given off as things fall into them.
• If the Sun were a black hole the Earth would still orbit it.
• The distance from the black hole where gravity is so strongthat even light cannot escape is called the event horizon orthe Schwarzschild radius.
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Parts of a black hole
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Clicker Question
What would happen to the event horizon of a
black hole if the mass were doubled?
a) it would be 4 times larger
b) it would be half as large
c) it would be one-fourth as large
d) it would double
e) it would stay the same
NOTE: event horizon and Schwarzschild radius are used
Interchangeably. ISP209s10 Exam3 Review -30-
Clicker Question
If the Sun suddenly became a black hole, what would happento the Earth’s orbit?
A). The Earth would start a spiral into the Sun
B). The Earth would fly off out of the solar system
C). Depending of the mass of the Sun, the Earth’s orbit wouldapproximately double or be approximately half of what it isnow
D). The Earth would join all the other plants at the sameradius from the black hole
E). Nothing
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Clicker Question
Which of the following is not evidence for
the existence of Black Holes?
A). The rotation speed of material around a
central object
B). Emission of large amounts of energy
C). Radio lobes of active galaxies
D). A blackbody spectrum of photons
ISP209s10 Exam3 Review -32-
Clicker Question
What causes QUASARS, which are very
bright (a 100 times the energy output of a
normal large galaxy) observed far from Earth?
A). Black holes
B). The Higgs Boson
C). The Big Bang
D). We don’t know
ISP209s10 Exam3 Review -33-
Clicker Question
What does entropy have to do with time?
A). We think conservation of entropy explains time
B). It is possible that early in the big bang inflationcreated a universe with too little entropy. Hence, allprocess tend toward increasing entropy and give time adirection.
C). It explains why quasars cause time to increase.
D). We know of no connection whatsoever.
E). The second law says time must always decrease.
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Wormholes
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Wormholes
• Wormholes are a possible solution to Einstein’sequations.
• If there are wormholes, there must be white holes.No white hole has ever been observed.
• We think a white hole is not stable since materialwould collect near the opening and collapse thewhite hole to a black hole.
• Some type of exotic material (that acts asantigravity) is necessary to keep the white holeend open.
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String Theory and the Standard Model
• “Standard Model” is a collection of the currently known particles andthe forces between them. It does not answer “Why”.
• The LHC at CERN is searching for the Higgs particle to explainwhere mass comes from and for dark matter.
• Know that science is trying to find one theory that describeseverything. Part of this quest is to understand how all the forces arerelated.
• Know that String Theory tries to describe everything in terms ofvibrating strings. The size of the strings is 10-35m.
• The minimum number of dimensions for M-theory to work is 11.
• We experience only 4 dimensions. The others are too small.
• String Theory as a whole has not yet made falsifiable predictions.Another problem with String Theory is the Landscape problem, whichis that sting theory may not explain why our Universe is as it is.
ISP209s10 Exam3 Review -37-
String Theory Pictures
Extra dimensions
What one of the
dimensions might
look like. Calabi-
Yau space
Interaction of strings:
The finite size (10-35m)
overcomes many of the
problems with the interaction of
point particles.
ISP209s10 Exam3 Review -38-
Other Standard Model and String Theory Stuff
• Understand how extra dimensions in String Theory might
explain why gravity is so weak.
• How might the actual Big Bang be explained by String
Theory?
• Know what the following physics “beyond the standard
mode” refers to
– Dark Matter and Dark Energy
– Higgs Boson and the origin of mass
– Supersymmetric theories
• Despite huge promise, String theory has some problems
– Is it experimentally testable? Connected with tiny size of strings
ISP209s10 Exam3 Review -39-
Atomic Nuclei
• Number of protons determines the atomic
number and chemical nature.
• The isotope is determined by the number of
neutrons.
• 14-C has 6 protons (that makes it carbon, C)
and 14-6=8 neutrons.
ISP209s10 Exam3 Review -40-
Half life
Radioactive decay is governed by the rules of probability. If we
start with N atoms, in the time of one half-life on average half will
have decayed. In the next half life, half of those remaining will
have decayed, and so on.
4
1
2
1)2(
2
2
1)(
2
0
0
21
21
21
=!"
#$%
&==
=
!"
#$%
&==
N
tNf
ttif
t
t
N
tNf
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Sample Problem
The amount of 14-C in an old sample is 0.125 of the
expected amount. How old is the sample? DATA:
Assume the half-life of 14-C is 6000 years.
A)6000 years
B)12,000 years
C)18,000 years
D)24,000 years
E)30,000 years
lives-half ofnumber
2
1)( 0 !
"
#$%
&= NtN
ISP209s10 Exam3 Review -42-
Example
A sample of radioactive material contains two types of nuclides,
that we call A and B. Nuclide A has a half-life of 4 hours and
Nuclide B has a half-life of 8 hours.
If at t = 0 the ratio of A/B = 1, what is the ratio at at t = 16 hours?
Use A0/B0 = 1 and !A = .693/TA1/2 and similarly for B.
ANS: A(t=16 hours)/B(t=16 hours) = .25
ISP209s10 Exam3 Review -43-
Half-life fraction table
10
.031255
.06254
.1253
.252
.51
Fraction, fTime (half-lives)
ISP209s10 Exam3 Review -44-
Other Stuff on Atomic Nuclei
Know the different types of radioactive decays (Beta-decay,
Alpha-decay, Gamma-decay, Fission)
Understand the principles of radioactive dating.
Know what nuclear fusion is, and understand why you need
High temperatures and densities to make it happen
ISP209s10 Exam3 Review -45-
Life in the Universe
• The one ingredient for life of Earth is liquid water
• Liquid water might be found on Mars, the moons
of Jupiter (e.g. Europa) and moons of Saturn
• The Drake Equation can be used to estimate the
number of technological civilizations we might be
able to communicate with
• Know what SETI is
ISP209s10 Exam3 Review -46-
Most of the Universe is Dark Matter
• There are three main pieces of evidence that there
is much more mass in the universe than that from
luminous matter.
– Gravitational lensing
– Rotation curves of galaxies
– Fluctuations in the cosmic microwave background
radiation
• It turns out that only 4% of the Universe is made
of the same stuff as us.
ISP209s10 Exam3 Review -47-
Gravitational Lensing results from General Relativity
ISP209s10 Exam3 Review -48-
Rotation Curves
Rotation implies
acceleration
The force that supplies
the acceleration is
gravity. More gravity
implies a faster rotation.
There is more rotation
and hence more gravity
than expected at large
radii.
ISP209s10 Exam3 Review -49-
Fluctuations in the Cosmic Background
WMAP observatoryImage of the universe at about 379,000
years after the Big Bang
ISP209s10 Exam3 Review -50-
What we have learned from WMAP
• Within a 1% accuracy (100 million
years) the Universe is 13.7 billion years
old.
• We don't know what 96% of the
Universe is made of.
• The first stars formed about 200 million
years after the Big Bang.
• The picture of the background
microwave radiation is from 379,000
years after the Big Bang.
• At the present it appears the Universe
will expand forever.
ISP209s10 Exam3 Review -51-
What are Dark Matter and Dark Energy?
• We don’t know.
• Dark energy actually acts like anti-gravity and is pushing
the universe apart. We can tell this because distance
supernova are moving away faster than they should.
• Dark matter is probably some type of undiscovered particle.
– These Particles may interact by the weak force (they do interact by
gravity)
– People are looking for WIMPs (Weakly interacting massive
particles)