•exam #3 is thursday 4/29 in this room •you can bring 2 page of...

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


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, whereasothers will have more.


Exam 3 review

• A detailed outline of study topics is here:

http://www.nscl.msu.edu/~bogner/isp209s2010/review3.htm


How do we measure properties of a star?

How do we know what oursun (and other stars) are madeof ?

How do we know thetemperature?

How do we know the size?

From the spectrum of the EM radiationfrom the star (“Blackbody radiation”)


Some Clicker Questions - #1

What happens to a star if its surface temperature is increased andits size remains the same?

A) It only gets brighterB) It only gets more redC) It gets brighter and more blueD) It only gets dimmerE) It gets dimmer and more red

Hint: recall how color correlates with temperature



What happens to a star if its surface temperature is increased andits size remains the same?

A) It only gets brighterB) It only gets more redC) It gets brighter and more blueD) It only gets dimmerE) It gets dimmer and more red

Remember the correlation between color andTemperature Blue: Hotter Red: Colder


Hertzsprung-Russell Diagram:How a star evolves

Luminosity vs.Temperature

Observed stars tendto fall on various “branches” in thisplot.

Which “branch” a starFalls on depends on How it generates itsEnergy (I.e., what Fusion chains occur)


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

#

#

##


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”.


How did the Universe Begin?

• Evidence points to the Universe beginning in a hotfireball 13.7 billion years ago. We call this the BigBang

• 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 earlyuniverse (mostly hydrogen and helium).

– The cosmic microwave background radiation


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 =!=


Big Bang Timeline (the early moments)


Inflation

Years since the Big Bang

Met

ers

The existence ofan unknownscalar fieldcaused the rapidinflation of theUniverse


Why does time always move in one direction?• Inflation during the Big Bang resulted in a

universe 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.


Clicker Question

• Which of the following events occurred earliestin the Big Bang? Choose the best answer.

A. hydrogen and helium were madeB. the era of inflation where universe grew by

1050 timesC. electrons combined with nucleiD. galaxies formedE. stars formed


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 have

evaporated• 101000 years the Universe will reach its

lowest energy state• Note: The current age of the Universe is

13.7 billion years 1010 years


Other Big Bang Stuff…

• Understand why the CMB radiation map is likelooking at a baby picture of the universe “only”379,000 years after the Big Bang

• Know why the splotchiness in the CMB isimportant to be consistent observed features of theuniverse

• Know the expansion of the universe is anexpansion of space itself

• Know how the evidence for the Big Bang wasdiscovered by accident



The lightest two elements in nature are hydrogen and helium.Where do we think most atoms of other elements made?

A) In the Big BangB) In StarsC) On planetsD) In space between stars



In the Big Bang, what was the inflationary epochA) It was the start of the Big BangB) It was the period when the Universe increased in size by

1050

C) It was the period when nuclei were madeD) It was the period when atoms where made



What do we think caused the Big Bang?A) A Big CrunchB) GravityC) A large explosionD) The weak force and many neutrinosE) We don’t know

(NOTE: There are some speculations in String Theory as to A possible cause)



What will happen in the future?A) We will have a Big CrunchB) We think the Universe will expand foreverC) We think the Universe will stop expanding and be stationary in

about 10 billion years


Clicker Question

What is our best guess on the current age of theUniverse, and when will all the stars have burnedout?A). 13.7 billion years, 10100 billion yearsB). 137 billion years, 1010 billion yearsC). 13.7 billion years, 1010 billion yearsD). 1370 billion years, 101000 billion years,E). 1.37 billion years, 1010 billion years


Escape Velocity

Earth

vThe velocity to completely escape thegravity of a planet is:

planet

planet

R

GMv

2=

Something interesting happens (black hole) when v = c.

Mass, m


Clicker Question

What would happen to the escape velocity ofa planet if the radius of the planet were 2times larger and the mass was the same?A.It would be √2 times largerB.It would be √2 times smallerC.It would be 2 times largerD.It would be 2 times smaller

planet

planet

R

GMv

2=


Clicker Question

What would happen to the escape velocity ofa planet if the mass of the planet were 4 timeslarger and the radius was the same?A.It would be √2 times largerB.It would be √2 times smallerC.It would be 2 times largerD.It would be 2 times smaller

planet

planet

R

GMv

2=


Black Holes

The “hole” in space is so deep thatlight can not escape.


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 solar

masses.– 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 is

15 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 strong

that even light cannot escape is called the event horizon orthe Schwarzschild radius.


Parts of a black hole


Clicker Question

What would happen to the event horizon of ablack hole if the mass were doubled?

a) it would be 4 times largerb) it would be half as largec) it would be one-fourth as larged) it would doublee) it would stay the same

NOTE: event horizon and Schwarzschild radius are used Interchangeably.


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 SunB). The Earth would fly off out of the solar systemC). Depending of the mass of the Sun, the Earth’s orbit wouldapproximately double or be approximately half of what it isnowD). The Earth would join all the other plants at the sameradius from the black holeE). Nothing


Clicker Question

Which of the following is not evidence forthe existence of Black Holes?A). The rotation speed of material around acentral objectB). Emission of large amounts of energyC). Radio lobes of active galaxiesD). A blackbody spectrum of photons


Clicker Question

What causes QUASARS, which are verybright (a 100 times the energy output of anormal large galaxy) observed far from Earth?A). Black holesB). The Higgs BosonC). The Big BangD). We don’t know


Clicker Question

What does entropy have to do with time?A). We think conservation of entropy explains timeB). 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.


Wormholes


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.


String Theory and the Standard Model• “Standard Model” is a collection of the currently known particles and

the forces between them. It does not answer “Why”.• The LHC at CERN is searching for the Higgs particle to explain

where mass comes from and for dark matter.• Know that science is trying to find one theory that describes

everything. 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.


String Theory Pictures

Extra dimensions

What one of thedimensions mightlook like. Calabi-Yau space

Interaction of strings:The finite size (10-35m)overcomes many of theproblems with the interaction ofpoint particles.


Other Standard Model and String Theory Stuff

• Understand how extra dimensions in String Theory mightexplain why gravity is so weak.

• How might the actual Big Bang be explained by StringTheory?

• Know what the following physics “beyond the standardmode” 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


Atomic Nuclei

• Number of protons determines the atomicnumber and chemical nature.

• The isotope is determined by the number ofneutrons.

• 14-C has 6 protons (that makes it carbon, C)and 14-6=8 neutrons.


Half lifeRadioactive decay is governed by the rules of probability. If westart with N atoms, in the time of one half-life on average half willhave decayed. In the next half life, half of those remaining willhave decayed, and so on.

4

1

2

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21

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Sample Problem

The amount of 14-C in an old sample is 0.125 of theexpected amount. How old is the sample? DATA:Assume the half-life of 14-C is 6000 years.

A)6000 yearsB)12,000 yearsC)18,000 yearsD)24,000 yearsE)30,000 years

lives-half ofnumber

2

1)( 0 !

"

#$%

&= NtN


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 λA = .693/TA1/2 and similarly for B.

ANS: A(t=16 hours)/B(t=16 hours) = .25


Half-life fraction table

10

.031255

.06254

.1253

.252

.51

Fraction, fTime (half-lives)


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 needHigh temperatures and densities to make it happen


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 beable to communicate with

• Know what SETI is


Most of the Universe is Dark Matter

• There are three main pieces of evidence that thereis much more mass in the universe than that fromluminous 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.


Gravitational Lensing results from General Relativity


Rotation Curves

Rotation impliesacceleration

The force that suppliesthe acceleration isgravity. More gravityimplies a faster rotation.

There is more rotationand hence more gravitythan expected at largeradii.


Fluctuations in the Cosmic Background

WMAP observatoryImage of the universe at about 379,000years after the Big Bang


What we have learned from WMAP

• Within a 1% accuracy (100 millionyears) the Universe is 13.7 billion yearsold.

• We don't know what 96% of theUniverse is made of.

• The first stars formed about 200 millionyears after the Big Bang.

• The picture of the backgroundmicrowave radiation is from 379,000years after the Big Bang.

• At the present it appears the Universewill expand forever.


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 distancesupernova 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)

•exam #3 is thursday 4/29 in this room •you can bring 2 page of...

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