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Notes 43 - Topic 6 - Atomic and Nuclear Physics

Notes 43 - Topic 6 - Atomic and Nuclear Physics - --------------------------------------------------------------------------------------- 7 .3.8 Nuclear Fission and Nuclear Fusion 7 .3.11 Problems involving Fission and Fusion reactions

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Notes 43 - Topic 6 - Atomic and Nuclear Physics

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  1. Notes 43 - Topic 6 - Atomic and Nuclear Physics ---------------------------------------------------------------------------------------- 7.3.8 Nuclear Fission and Nuclear Fusion 7.3.11 Problems involving Fission and Fusion reactions (...are found in the previous sample problems and in the problems sets) FISSION • In 1938, Otto Hahn and Fritz Strassmann, German scientists, discovered that when Uranium was bombarded by neutrons some of the products were smaller nuclei that were about half the size of the uranium nucleus. • Lise Meitner and Otto Frisch (two Jewish refugees from Nazi Germany living and working on the same problem in Scandinavia) very quickly realized that the smaller nuclei were the result of the splitting of the uranium nucleus into two almost equal parts. This was an amazing realization because, until that time, the only known nuclear reactions involved knocking out a small particle (alpha, beta, positron) from a nucleus.

  2. • Typical Reactions: U-235 is bombarded by a neutron producing U-236 which is extremely unstable and undergoes fission to produce Xe-144, Sr-90, and 2 additional neutrons (show reaction in NB): U-235 is bombarded by a neutron producing U-236 which is extremely unstable and undergoes fission to produce Ba-141, Kr-92, and 3 additional neutrons (show reaction in NB): The process was named fission by Meitner and Frisch because it so closely resembled the biological process of mitosis which produces similar “daughter” cells.

  3. 2 a i. fission: massive unstable nucleus splits into two more stable nuclei decay: unstable nucleus emits particles to make it more stable 2 a ii. U + n --> Sr + Xe + 4 n 235 92 1 0 90 38 142 54 1 0 2 a iii. β- no charge in mass number but the atomic number increases by 1

  4. (1/2)mv2 = p2/(2m) 2 b i. KE = 102 MeV = p2/2m p2=(102MeV ) 2m p = √ (102MeV (2) m) p = √ (102MeV)(1.6x10-13) (2) 90(1.66x10-27kg) psr=2.2089x10-18Ns pxe = 2.2149x10-18 Ns

  5. • Nuclear Fission releases a tremendous amount of energy on an atomic level for only one nuclear event... Binding Energy per nucleon of Barium-141 = 8.5 MeV nuc-1 - Binding Energy per nucleon of Uranium-235 = 7.6 MeV nuc-1 __________________________________________________ Difference = 0.9 MeV nuc-1 • Each fission event produces a nucleus with a higher binding energy per nucleon and thus a more stable nucleus. Since Uranium-235 has 235 nucleons, energy released ≈ 200 MeV per fission!! (typical chemical reactions release about 1 eV per atom) • NOTICE... each fission releases additional neutrons; if these neutrons are captured by other uranium nuclei, a chain reaction would be created which would release huge amounts of energy on a macroscopic level;

  6. Sample Problem 1: U-235 is bombarded by a neutron, undergoes fission, and produces Ba-141, Kr-92, and 3 additional neutrons. Determine the amount of energy released from this fission reaction. mU = 235.043930 u mBa = 140.914411 u mKr= 91.926156 u mn = 1.008665 u Given: Uknown: Equation:

  7. Non-Required Notes and Information • Enrico Fermi, an Italian physicist who was a refugee from Mussolini’s regime, theorized that the neutrons released by the fission reaction were moving too fast to be captured by other uranium nuclei. He decided to put dense materials in and around the uranium-235 to decrease the neutrons’ speed...a moderator. On December 2, 1942, under the football grandstand at the University of Chicago, Fermi produced the first self-sustaining nuclear fission reaction using cadmium rods as the moderator. • Requirements for a Self-sustaining, Controllable Nuclear Fission Reaction: 1. The Right Stuff - Uranium-235 is the fissionable isotope but it only occurs as 0.7% of natural uranium deposits; it is usually enriched to at least 5% for power plant use; nuclear weapons require nearly 100% purity; 2. Critical Mass - a few kilograms of 5% U-235; 3. Control Rods - reduces neutron speed and/or absorbs neutrons to vary the rate of the chain reaction;

  8. Non-Required Notes and Information • Evidence ofat least 6 Natural Nuclear Reactors that occurred 4 km underground in West Africa over 2 billion years ago were discovered by French scientists in 1972. This could only have happened as a result of the spontaneous fission of U-235 or U-238 and a self-sustaining chain reaction in each location. Simulated Chain Reaction http://lectureonline.cl.msu.edu/~mmp/applist/chain/chain.htm Mousetrap Reactor http://www.ap.smu.ca/demos/content/modern/mousetrap_reactor/mousetrap_reactor.html Nuclear Power Plant http://people.howstuffworks.com/nuclear-power2.htm

  9. Non-Required Notes and Information

  10. Non-Required Notes and Information In reference to the Trinity test in New Mexico, where the first atomic bomb was detonated, Oppenheimer famously recalled the Bhagavad Gita: "If the radiance of a thousand suns were to burst at once into the sky, that would be like the splendor of the mighty one... Now, I am become Death, the destroyer of worlds." • Temperatures generated during an atom bomb explosion approach 20 million K; the heat energy and radioactive isotopes produced during the process are released into the environment. A-Bomb History (short) http://www.spartacus.schoolnet.co.uk/2WWatom.htm The First 2 Bombs http://www.atomicarchive.com/Fission/Fission6.shtml

  11. FUSION • Fusion is the process by which two low mass nuclei combine to form a more massive nucleus; this is possible because, up to iron (Fe), high mass nuclei have a higher binding energy per nucleon and are thus more stable than the low mass nuclei. Example: hydrogen nucleus (proton) combines with a neutron to form deuterium and a gamma ray Calculation: 1 x proton = 1.007827 u 1 x neutron = 1.008665 u ___________________________ Expected mD = 2.016490 u -Actual mD = -2.014102 u ___________________________ Mass Defect = 0.002388 u Energy Released = (0.002388 u) (931.5 MeV u-1) Energy Released = 2.22 MeV per fusion

  12. Sample Problem 2: At high temperature and pressure, a deuterium nucleus fuses with a tritium nucleus to produce a helium-4 nucleus and a free neutron. (A) Write the equation for this reaction. (B) Determine the amount of energy released. mD = 2.013553 u mT = 3.016049 u mHe = 4.002603 u mn = 1.008665 u (A) (B) Given: Unknown: Equation: ...

  13. • Requirements for a Nuclear Fusion Reaction: 1. The Right Stuff - low mass nuclei (the lower the mass the easier to cause...hydrogen nuclei are the “easiest” to fuse); 2. Extremely High Temperature - 1 x 108 K; 3. Extremely High Pressure - millions of Pa; • Fusion Power - Scientists have been trying to develop fusion power for the generation of electricity for 30+ years with little success. Here is a site with info about the research and the problems... Fusion Power http://www.fact-index.com/f/fu/fusion_power.html#Power%20plant%20design

  14. Non-Required Notes and Information • The Hydrogen Bomb - temperatures produced by A-bomb explosions approach the needed temperatures to cause a fusion reaction to begin. The H-Bomb (thermonuclear weapon) is 2 bombs in 1...a fission bomb is exploded to generate high temperature and pressure and those conditions are used to cause a fusion reaction. The H-Bomb http://whyfiles.org/186ed_teller/3.html • The Neutron Bomb - a thermonuclear weapon designed to produce as many high speed neutrons as possible but have as small a blast as possible; the neutrons penetrate virtually all matter, even the densest tank armor, and can provide a lethal dose of radiation to living organisms that are kilometers from the actual blast. The N-Bomb (and others) http://nuclearweaponarchive.org/Library/Brown

  15. 7.3.9 Applying the Binding Energy per Nucleon Curve Draw by hand, and annotate, on a full page of graph paper, a graph of binding energy per nucleon as a function of atomic number (Z) or as a function of mass number (A), and apply it to predict nuclear energy changes for fission and fusion; Examples of the graph are found in both textbooks and the website listed... Binding Energies and Mass Number http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html WHY DO FISSION AND FUSION TAKE PLACE? Simple...the results of each are more stable!! • Notice the curve peaks about A = 60...this is the Iron Group and these nuclei are the most stable; • Elements to the left tend to undergo fusion and elements to the right tend to undergo fission; • Fusion for a less massive nucleus and fission for a more massive nucleus produces a more stable nucleus; • Elements in the iron group will undergo neither fission nor fusion under “normal” conditions;

  16. 7.3.11 Nuclear Fusion...the primary source of the Sun’s energy • In 1939, physicist Hans Bethe, a refugee from Nazi Germany, proposed the proton-proton cycle as the primary source of energy for stars similar to the Sun: 1. A proton combines with another proton to form deuterium, a positron, a neutrino, and release 0.42 MeV of energy; (show equation in NB) 2. The deuterium combines with another proton to form He-3, a gamma ray, and release 5.49 MeV of energy; (show equation in NB) 3. 2 He-3 nuclei combine to form one He-4, 2 protons, and release 12.86 MeV of energy; (show equation in NB) Each of the first two reactions happen twice to allow the 3rd reaction to occur; the net reaction for the proton-proton cycle: 4 protons combine to form 1 He-4, 2 positrons, 2 neutrinos, and 26.7 MeV of energy* (*2.02 MeV of extra energy comes from the annihilation of the positrons meeting free electrons after their production) In Sol (our star), 685 MTon (6.85 x 1011 kg) of matter is converted into energy each second by the nuclear fusion of H into He.

  17. Non-Required Notes and Information • The “natural limit” for the production of more massive nuclei by stellar fusion is the Iron (Fe) Group; notice on your Binding Energy graph that Fe (actually Ni-62) has the highest binding energy per nucleon, and more massive nuclei cannot be produced under normal stellar conditions; • Normal stellar conditions are surpassed during a Supernova Explosion. During these most powerful of all naturally occuring events, temperatures and pressures far surpass the natural limits for even the largest blue-giant stars and make the production of all more massive nuclei through uranium possible; • All naturally occuring elements in the universe are produced through the nuclear fusion reactions in stars; the elements more massive than the Iron Group are produced only during Supernova Explosions; all matter is made of “star dust!!”

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