Exam #3 Exam #3 is Thursday 4/9 in this room You can bring page of notes (front and back) Bring your calculator and a # 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 4/9 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. ISP09s10 Exam3 Review -1- ISP09s10 Exam3 Review -- Exam 3 review A detailed outline of study topics is here: http://www.nscl.msu.edu/~bogner/isp09s010/review3.htm 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 ) ISP09s10 Exam3 Review -3- ISP09s10 Exam3 Review -4-
Some Clicker Questions - #1 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 ISP09s10 Exam3 Review -5- 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 ISP09s10 Exam3 Review -6- Hertzsprung-Russell Diagram:How a star evolves Luminosity vs. Temperature Observed stars tend to fall on various branches in this plot. ISP09s10 Exam3 Review -7- 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 luminosity brightness = 4# (distance) Which branch a star a Falls on depends on How it generates its ba 4# da db = = = 5 " d Energy (I.e., what b = 5! d a b L b b da Fusion chains occur) ISP09s10 Exam3 Review -8-4# db L L = 4# d
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 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 ISP09s10 Exam3 Review -9- ISP09s10 Exam3 Review -10- Hubble Expansion Big Bang Timeline (the early moments) Hubble observed that on average all galaxies seem to be moving away from us. The speed is related to distance. Galaxies farther away are moving faster Hubble Law: km / s velocity = H0! distance; H0 = 0 Mly If a galaxy is observed to be moving away at 000 km/s, we expect the galaxy is v/h 0 =100 Mly away ISP09s10 Exam3 Review -11- ISP09s10 Exam3 Review -1-
Meters Inflation Years since the Big Bang The existence of an unknown scalar field caused the rapid inflation of the Universe Why does time always move in one direction? Inflation during the Big Bang resulted in a universe that had a very low entropy. Much too low for its size. Hence, everything in the Universe moves toward reaching the correct amount of entropy. Time has a direction because going back in time would imply the entropy could be decreased. ISP09s10 Exam3 Review -13- ISP09s10 Exam3 Review -14- 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 10 50 times C. electrons combined with nuclei D. galaxies formed E. stars formed ISP09s10 Exam3 Review -15- What is the Ultimate Fate 10 100 years all the stars will have used their fuel 10 100 to 10 150 years dark ages 10 150 years all black holes will have evaporated 10 1000 years the Universe will reach its lowest energy state Note: The current age of the Universe is 13.7 billion years 10 10 years ISP09s10 Exam3 Review -16-
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 accident ISP09s10 Exam3 Review -17- 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 ISP09s10 Exam3 Review -18- Some Clicker Questions - # Some Clicker Questions - #3 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 10 50 C) It was the period when nuclei were made D) It was the period when atoms where made 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) ISP09s10 Exam3 Review -19- ISP09s10 Exam3 Review -0-
Some Clicker Questions - #4 Clicker Question 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 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, 10 100 billion years B). 137 billion years, 10 10 billion years C). 13.7 billion years, 10 10 billion years D). 1370 billion years, 10 1000 billion years, E). 1.37 billion years, 10 10 billion years ISP09s10 Exam3 Review -1- ISP09s10 Exam3 Review -- Escape Velocity Clicker Question Mass, m v Earth The velocity to completely escape the gravity of a planet is: v = GM R planet planet Something interesting happens (black hole) when v = c. What would happen to the escape velocity of a planet if the radius of the planet were times larger and the mass was the same? A.It would be! times larger B.It would be! times smaller C.It would be times larger D.It would be times smaller v = GM R planet planet ISP09s10 Exam3 Review -3- ISP09s10 Exam3 Review -4-
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! times larger B.It would be! times smaller C.It would be times larger D.It would be times smaller v = GM R planet planet Black Holes The hole in space is so deep that light can not escape. ISP09s10 Exam3 Review -5- ISP09s10 Exam3 Review -6- 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 ISP09s10 escape Exam3 Review is called the event horizon -7- or the Schwarzschild radius. Parts of a black hole ISP09s10 Exam3 Review -8-
Clicker Question 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. ISP09s10 Exam3 Review -9- If the Sun suddenly became a black hole, what would happen to 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 would approximately double or be approximately half of what it is now D). The Earth would join all the other plants at the same radius from the black hole E). Nothing ISP09s10 Exam3 Review -30- 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 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 ISP09s10 Exam3 Review -31- ISP09s10 Exam3 Review -3-
Clicker Question Wormholes 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 inflation created a universe with too little entropy. Hence, all process tend toward increasing entropy and give time a direction. 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. ISP09s10 Exam3 Review -33- ISP09s10 Exam3 Review -34- Wormholes Wormholes are a possible solution to Einstein s equations. 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 material would collect near the opening and collapse the white hole to a black hole. Some type of exotic material (that acts as antigravity) is necessary to keep the white hole end open. ISP09s10 Exam3 Review -35- 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 are related. Know that String Theory tries to describe everything in terms of vibrating strings. The size of the strings is 10-35 m. 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, which is that sting theory may not explain why our Universe is as it is. ISP09s10 Exam3 Review -36-
String Theory Pictures Other Standard Model and String Theory Stuff Extra dimensions What one of the dimensions might look like. Calabi- Yau space Interaction of strings: The finite size (10-35 m) overcomes many of the problems with the interaction of point particles. 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 ISP09s10 Exam3 Review -37- ISP09s10 Exam3 Review -38- 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. ISP09s10 Exam3 Review -39- 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. N( t) & 1 # f = = $! N0 % " if t = t ) & 1 # = $! % " 1 4 ISP09s10 Exam3 Review -40-1 N(t f = N 0 1 t t 1 =
Sample Problem The amount of 14-C in an old sample is 0.15 of the expected amount. How old is the sample? DATA: Assume the half-life of 14-C is 6000 years. A)6000 years B)1,000 years C)18,000 years D)4,000 years E)30,000 years number of half - lives & 1 # N( t) = N0 $! % " ISP09s10 Exam3 Review -41- 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 A 0 /B 0 = 1 and! A =.693/T A 1/ and similarly for B. ANS: A(t=16 hours)/b(t=16 hours) =.5 ISP09s10 Exam3 Review -4- Half-life fraction table Other Stuff on Atomic Nuclei Time (half-lives) 0 1 3 4 Fraction, f 1.5.5.15.065 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 5.0315 ISP09s10 Exam3 Review -43- ISP09s10 Exam3 Review -44-
Life in the Universe Most of the Universe is Dark Matter 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 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. ISP09s10 Exam3 Review -45- ISP09s10 Exam3 Review -46- Gravitational Lensing results from General Relativity 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. ISP09s10 Exam3 Review -47- ISP09s10 Exam3 Review -48-
Fluctuations in the Cosmic Background Image of the universe at about 379,000 years after the Big Bang What we have learned from WMAP WMAP observatory ISP09s10 Exam3 Review -49- 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) ISP09s10 Exam3 Review -51- 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 00 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. ISP09s10 Exam3 Review -50-