Fission and fusion. E = mc 2 Mass is another form of energy a nucleus is lighter than the sum of the constituent particle masses

Transcription

1 Fission and fusion The strong force causes nucleons to attract each other. When nucleons combine into nuclei, energy is released. This is called the binding energy. Iron is the most tightly bound so if we can make elements up to Iron by the fusion of light elements energy is released. Similarly if we can break a very heavy atom into lighter elements we also have energy release. E = mc 2 Mass is another form of energy a nucleus is lighter than the sum of the constituent particle masses Fusion processes are how the sun produces energy and fission processes are how nuclear reactors produce energy 1

2 Chain reaction If a U 235 atom is broken into two lighter elements energy is released. This is accomplished using a neutron. The process produces 3 neutrons which, if they don t escape, can then cause 3 more atoms to undergo fission. Without any control this chain reaction produces an enormous amount of energy in a fraction of a second. It is a (mis-named) atomic bomb really a nuclear bomb. This process was first observed by Enrico Fermi in a laboratory under the Chicago University football stadium U 235 2

3 Manhattan project and the bomb In the early forties many top scientists were recruited to Los Alamos to design the atomic bomb. In order for a bomb to work there had to be sufficient Uranium 235 but it could not be stored in one piece because runaway fission would spontaneously occur. The main challenges were to obtain enough U 235 and to design a system to bring the uranium together very quickly with a neutron source after the bomb was dropped. 3

4 Manhattan project and the bomb U 235 is separated from U 238 in various ways: Gaseous diffusion of UF 6 : the lighter isotope diffuses very slightly faster than the heavier isotope. Many stages and huge electric power are required. Centrifuges, spinning very rapidly, cause the heavier U 238 to separate slightly from the U 235. Again, many stages of separation are required 4

5 Manhattan project and the bomb The Plutonium bomb had a different way of obtaining the critical mass : the Plutonium was completely assembled into a sub-critical sphere, and surrounded by a spherical shell of explosives. After the bomb is dropped, the explosives are detonated very precisely to send a shock wave inward, which compresses the Plutonium so densely that it achieves critical mass. 5

6 Manhattan project and the bomb Plutonium is separated chemically from spent fuel rods from nuclear reactors. This is easier than separating U isotopes except for the fiercely radioactive fission products. There is also the risk that a critical mass of Plutonium could accumulate in the pipes or vessels of the separation plant. 6

7 The hydrogen (fusion) bomb Fusion gives a much bigger energy release than fission, Hydrogen bombs are designed to use an atomic bomb to provide the temperature and pressure so that fusion takes place. There is a central core of light elements surrounded by plutonium or uranium. 7

8 Enrichment Naturally occurring uranium is nearly all U 238 U 235 is the fissionable material. Enrichment means increasing the fraction of U 235,. For a reactor the final fraction of U 235 is about 3.5%, which allows light water H 2 O to be the neutron moderator, slowing the neutrons down until they react strongly with the U 235 For the original bomb several kilograms of much closer to 100% enriched U 235 were required. 8

9 Alternative to Enrichment Use Plutonium from reactors: Notice that once a neutron is added to U 238, all the isotopes have A=239, but beta decay keeps increasing the value of Z, by changing n into p. 9

10 LEARNING QUIZ In the above example, IF 94 Pu 239 were to decay by alpha particle emission, what Element and Isotope would be the daughter nucleus? A.Thorium B. Uranium C. Neptunium D. Plutonium E. Americium 10

11 Nuclear reactors In order to produce energy we need to have controlled fission. Fuel rods are inserted into a moderator, which is used to slow the neutrons down and not let them escape. U 235 absorbs slow neutrons much more readily than fast ones. Control rods are used to absorb neutrons to keep the chain reaction from running away disastrously. The control rods can be moved in and out to set the level of energy production including shutting the reactor off completely. The energy is taken out as heat, with a circulating liquid, and steam is generated to drive a turbine. 11

12 Toxic disposal, other hazards Most of the elements produced in the fission process are highly radioactive. All materials inside the containment vessel also become highly radioactive. Disposal of this toxic nuclear waste is a challenge since it must not enter the environment. There is controversy over a proposed waste disposal site at Yucca mountain. In 1986 operator error at the Chernobyl nuclear plant caused an uncontrolled chain reaction. The resulting release of radiation had effects over almost all the northern hemisphere and thyroid cancer rates have increased 10 fold in the Ukraine. The design of this GRAPHITE-moderated reactor is totally different from the pressurized-water reactors used in the US. The graphite reactor tends to run away when it gets hot, and is therefore intrinsically unstable. The water reactors LOSE neutronmoderating ability when they overheat, and this prevents a runaway nuclear chain reaction. 12

13 Radiation in everyday life We are exposed to radiation at low levels from a number of sources Cosmic rays Radon and other natural radioactivity Medical imaging Consumer products fire alarms Radiation is also used to treat cancer PET scans All kinds of medical tracers e.g. radioactive iodine Used in industry to measure and then control thickness of rolled steel and paper Sterilization of food: can kill all manner of pathogens with little effect on the food itself. 13

14 Announcements Clickers will be used only for attendance this week. The final exam is Saturday of Exam Week 14

15 Announcements Remember that your own personal crib sheets are encouraged. For the final exam, 3 sheets = 6 sides is the guideline. 15

16 Fusion as an energy source Every second the sun turns 600 million tons of hydrogen into 596 million tons of helium (with 4 million tons transformed into luminous energy via E=mc 2 ). To emulate the sun we need extremely high temperatures and pressures to squeeze light elements together. Livermore National lab has tried to do this using high power (Terawatt) laser beams to compress (implode) small pellets of deuterium and tritium. There is an international effort based in France called ITER to try to produce controlled fusion using magnetic-field confinement of very hot plasmas ( soups of ionized atoms and electrons). Unfortunately, the US cut back severely on funding of the US effort in this collaboration two years ago, although we later restored the funding. 16

17 Fusion as an energy source First figure shows the reaction of 1D T 3 to give 2 He 4 and a neutron. Notice that the neutron has four times the energy of the He. This is our old friend the bullet and gun -- conservation of momentum result: the light projectile takes most of the available Kinetic Energy, and the sharing ratio is just the inverse of the mass ratio, 4:1 in this case. Unfortunately, the neutrons tend to make the reaction vessel radioactive (by transmutation, adding excess neutrons relative to the p vs. n curve of stability. Also, Tritium itself is radioactive, and, like Hydrogen, hard to keep from leaking. It would be better to react D+D, but this requires a higher ignition temperature and density. 17

18 Fusion as an energy source Second figure shows the laser-driven inertial confinement arrangement, with symmetrical ports for multiple laser beams. The idea is to symmetrically implode tiny metal-coated glass spheres containing a gas of compressed D & T. Like for the much larger Plutonium bomb, it is essential for the implosion to be spherically symmetrical to obtain very high compressions. The laser heats and vaporizes the capsule, which explodes outward and, by inertial recoil (Newton s 3d law) the gas is driven inward toward the center. This is similar to what happens in a supernova explosion of a star (in which, by the way, heavy elements are created by neutron bombardment of lighter elements, followed by beta decays.) 18

19 Summary of Chapters 18 and 19 n # electrons 1 2n 2 = 2 2 2n 2 = 8 3 2n 2 = n 2 = 32 TELEVISION: The accelerating voltage is typically 30,000 volts and X rays are produced as the beam hits the screen 19

20 Periodic table The nucleus Decay Chain reaction E = mc 2 20

21 Relativity for spectators Since c (speed of light) can be derived from the equations of electricity and magnetism, and we suppose that the laws of physics should be independent of which moving system the observer is in (provided the moving system is UNACCELERATED, so it s called an inertial system ) It follows that the speed of light should be the same in all systems. This violates our everyday intuition about relative velocities: light emitted from a moving system isn t any faster than light emitted from a system at rest [At rest relative to an observer] 21

22 Relativity for spectators If the speed of light is the same in all systems: Moving objects appear to get shorter along their direction of motion (relative to the observer). Moving clocks (or organisms) seem to have their time run slower. Velocities do not add in a simple linear fashion. A flashlight moving at half the speed of light, c/2, relative to the Earth, emits a beam of light with speed c (as seen from Earth.) An observer moving WITH the flashlight ALSO sees the beam moving with c. Velocities no longer add linearly. v = (v 1 +v 2 ) / (1 + v 1 v 2 /c 2 ) This matters only if at least one velocity is LARGE 22

23 Relativity for spectators v = (v 1 +v 2 ) / (1 + v 1 v 2 /c 2 ) If v 1 = c/2 is flashlight s speed, v 2 = c is speed of light RELATIVE to flashlight, and c is the light speed observed from Earth, the formula gives: v = 1.5 c / ( c x c/c 2 ) = 1.5 c / 1.5 = c So the new formula works exactly even at light speeds. And if v 1 and v 2 are each 1% the speed of light, the error of the simple linear formula v = (v1+v2) is only one part in

24 Relativity for spectators Easy to check that adding c to c gives c!! Etc. THERE S MORE: If the speed of light is the same in all systems: Momentum p = mv/ 1 ( v/ c) 2 TOTAL energy E = mc 2 2 / = Rest E + KE 1 ( v/ c) Rest mass is equivalent to energy mc 2 = Rest E For v/c<<1, the KE reduces to ~~Newtonian mv 2 /2 For v=0, KE is 0 and Total E = mc 2 = Rest Energy 24

25 Relativity for spectators As v c, (1-v 2 /c 2 ) 0, sqrt() 0, and 1/sqrt() 1 / 0 grows without bound. So v=c is physically impossible (except for zero-mass particles like PHOTONS) This factor 1/sqrt(1-v 2 /c 2 ) = 1/ 1 ( v/ c) 2 is what allows the Energy and Momentum of a particle to increase without bound, while the SPEED gets arbitrarily close to c but can never reach c (or E and p would become infinite.) 25

26 Relativity for spectators The factor sqrt(1-v 2 /c 2 ) = Rest E / Total E also tells us exactly how much a clock in a moving system slows down. For example, at Fermilab we have beams of 140 GeV pions (nuclear force particles that glue nucleons together) which can travel for over a mile. Pions have radioactive decay lifetimes of 2.2 x 10-8 s, and rest mass of 140 MeV/c 2. At close to c, you d think the pions could, on average, go only 3x10 8 m/s x 2.2x10-8 s = 6.6 meters!! But the time dilation factor is 0.14GeV/140GeV = 1/1000. So the pions go, on average 6,600 meters before decaying. Everyday experience at Fermilab tells us Einstein was absolutely correct. 26

27 Relativity for spectators The factor sqrt(1-v 2 /c 2 ) = Rest E / Total E also tells us exactly how much a moving object appears to shrink along the direction of its motion. As seen by the PIONS, the Laboratory appears to shrink, and the 6.6 km beamline seems to be only 6.6 m long, which is consistent with the pion s decay lifetime IN ITS OWN REST SYSTEM. 27

28 The twin paradox The factor sqrt(1-v 2 /c 2 ) = Rest E / Total E tells us how much a clock in a moving system slows down. Bill gets in a spaceship and travels at 0.99c to Alpha Centauri, the nearest star, which is 4 light-years away (it takes light that long to get to us from this star.) Bill stops, takes a quick look around, trying to find any possible planets, then starts back home at 0.99c. Bill s twin sister Abigail stays home. For Abigail, it takes a little over 8 years for Bill to make the round trip. But Bill s body clock has slowed down during the trips, by a factor sqrt( ) ~~ sqrt(1-.98) = sqrt(0.02) ~~0.14 So to Bill, the trip lasted 0.14 x 8.08 years = 1.13 years. Bill comes back almost 7 years younger than Abigail!! 28

29 The twin paradox Once Bill returns he is almost 7 years younger than Abigail What if Bill had gone to a star 40 light years away? To him the trip would have taken 11.3 years and he would come back almost 70 years younger than Abigail. Such very fast trips are impractical: the factor 1/sqrt() = 1/0.14 ~~7 This means Bill (and his spaceship) would have to somehow gain kinetic energy equal to ~ 6 times their rest masses. This is COLOSSAL, and we have no technologies remotely approaching this capability. (The round trip would require losing this energy at Alpha Centauri, then gaining this energy for the return trip, then losing it again.) No way, Jose. 29

30 How fast can we go? Such very fast trips are impractical. What if we wanted to travel at 1% of c instead of 99% of c? v = m/s v/c = 0.01 KE + RestE = RestE/sqrt( ) ~~ RestE( / 2) KE = RestE x is still a great deal of energy Let mass of spaceship be 20 Tons (rather skimpy) KE = ( kg x m 2 /s 2 ) x = J x KE = J How much power acting for one day? J = 86,400 s x P P = Watts ~~0.7 TW That s about 700 1GW nuclear power plants going full blast. And no known reasonable way to transfer the necessary momentum and energy to the spaceship. 30

31 NEXT TIME First, please click your attendance now as soon as I enable the receiver. REVIEW SESSION will include discussion of the CRIB SHEET from the Final Exam, and indications of the balance and topics of the 28 questions. I ll post this week s lecture, and the crib sheet if possible, later today 31