Engineering energy in nuclear reaction.pptx

Energy in nuclear reaction

1. ENERGY CHANGES IN NUCLEAR REACTION

2. Lecture outline Change of Energy Binding Energy Theories/Principles : Nuclear fission and fusion

3. Mass and Energy relation Energy in nuclear reaction is under the purview of Einstein’s Theory of Relativity. According to Albert Einstein: energy is directly proportion to mass ….. If a system loses mass it loses energy (exothermic) If a system gains mass it gains energy (endothermic) Its mathematic equation: E = m c 2 c = speed of light (3 x 10 8 m/s) c 2 = 9 x 10 16 m 2 /s 2 ---- it has a large value that changes the relation between the mass and energy small changes in mass can cause a large changes in energy. MASS and ENERGY changed in nuclear reactions are much greater than in chemical reactions.

4. Change in Mass, Δ m and change in energy, Δ E Spontaneous nuclear reaction: products weigh less than the reactants Δ m, change of mass is negative (the sign of is Δ m negative) Δ E, change of energy : products is less than the energy of the reactants energy is evolved to the surrounding

5. Change of Mass-Energy Relations The energy change accompanying a nuclear reaction can be calculated from the equation: Δ E = c 2 Δ m Where: Δ E = change in energy , kJ/mol = energy of products – energy of reactants c = (3 x 10 8 m/s) , is the speed of light , constant c 2 = 9 x 10 16 m 2 /s 2 Δ m = change in nuclear mass , g/mol = summation of the nuclear mass in products side per mole minus summation of nuclear mass in reactants side per mole = ∑m(product/s side)(no. of moles) – ∑m(reactant/s side)(no. of moles) (no. of moles = equivalent from the coefficient in the balanced equation) NOTE: USE THE TABLE OF NUCLEAR MASS

6. Nuclear mass Nuclear mass

7. Nuclear mass Nuclear mass

8. Units of energy, kJ/mol: Derivation of unit of energy Δ E = c 2 Δ m = m 2 .g/s 2 . mol simplify: c = 3.00 x 10 8 m/s c 2 = (3.00 x 10 8 m/s) 2 c 2 = 9.00 x 10 16 m 2 /s 2 Δ E = 9.00 x 10 16 m 2 /s 2 Δ m But: 1 J = 1 kg. m 2 /s 2 1 m 2 /s 2 = 1 J/kg Δ E = 9.00 x 10 16 J/kg Δ m Δ E must be in kJ/g then convert units to kJ/g Δ E = 9.00 x 10 16 J/kg x 1 kg/1000 g x 1 kJ/1000 J ( Δ m) Δ E = 9.00 x 10 10 kJ/g Δ m Where: Δ E in kJ/mole Δ m in g/mole

9. Example: 82 Pb 206 + n 1  82 Pb 207 Calculate the change of energy per mole, Δ E, of 82 Pb 206 from the given nuclear reaction Given: Rqd .: Solution: answer: Δ E = – 6.543 x 10 8 kJ/mol

10. Sample problems: 2. Find the change of energy, Δ E per mole and Δ E per gram of the decay Pu for the nuclear reaction given: 94 Pu 239 → 2 He 4 + 92 U 235 Given: Rqd .: Solution: answers: ∆E = – 5.13 ×10 8 kJ/mole ∆E per gram = − 2.14644 × 10 6 kJ/g

11. Problem: 3. For the radioactive decay of radium – 226 , calculate the change of energy, Δ E in kJ when 10.2 g of radium decays by alpha particle. Given: Rqd : Solution: answer: Δ E in kJ = – 2.15283 x10 7 kJ

12. Comparison of energy release between nuclear reaction and ordinary chemical reaction. Ordinary chemical reactions: it needs only 50 kJ/g for a reaction to occur Nuclear reactions: it needs huge energy for a reaction to occur (much more than 50 kJ/g)

13. Nuclear mass Nuclear mass

14. Nuclear mass Nuclear mass

15. Nuclear Binding Energy energy required to separate a nucleus into its nucleons (nucleons = protons + neutrons) involve of decaying a parent isotope by proton and neutron emission Nuclei/nucleus of the atom contains : protons and neutrons energy required to break up the neutron and proton in the nucleus The mass of the nuclei/nucleus weighs less than the sum of the individual masses of the neutrons and protons. (1930)

16. Nuclear Binding Energy The mass nuclei/nucleus weighs less than the sum of the individual masses of the neutrons and protons. (1930) Example : 2 He 4 for 1 mole mass of the nucleus He is 4.0015 g (from the table) for individual mass of neutrons and protons use this equation to determine the number of neutrons: A = p + n It contains: 2 protons and 2 neutrons protons + neutrons are called nucleons The nuclear mass of proton is 1.00728 (2) = 2.01456 g The nuclear mass of neutron is 1.00866 (2) = 2.01732 g Total nuclear mass of proton and neutron = 4.03188 g (nucleons) Mass difference (mass defect) = mass of nucleons – mass of nucleus = 4.03188 g – 4.0015 g = 0.030388 g

17. Nuclear Binding Energy Mass defect --- difference in mass between the nucleus and the mass of the nucleons Nuclear Binding Energy --- energy required to separate a nucleus into its nucleons The mass defect leads to the binding energy, which holds the nucleus together

18. Nuclear Binding Energy: calculation Mathematical equation of Binding energy, Δ E Δ E = 9.00 x 10 10 kJ/g Δ m In binding energy: The products of the nuclear decay are the nuclear particles of protons and neutrons Δ m; Mass defect = the sum of the individual nuclear masses of the neutrons and protons minus nuclear mass of nucleus, = nuclear mass ( n+p ) – nuclear mass of nucleus = nuclear mass of nucleons – nuclear mass of nucleus Where: n = nuclear mass of neutrons in g/mole p = nuclear mass of protons/hydrogen in g/mole n + p ……. called nucleons mass of nucleus = nuclear mass of the parent isotope

19. Nuclear Stability and the Binding Energy Binding energy per mole of nucleons Divide the binding energy, Δ E by the number of nucleons Δ E/ no. of nucleons Answer: Δ E/ mol. of nucleon = 5.1555 X 10 8 kJ/mol

20. Example: 1. Binding Energy of Lithium-6 and the binding energy per mole of nucleons 3 Li 6  Given: Rqd : Solution: answer: Δ E = 3.0933X 10 9 kJ/mol Δ E/ mol. of nucleon = 5.1555 X 10 8 kJ/mol

21. Example: 2. Calculate the nuclear binding energy of C-14 in kilojoules per mole and the binding energy per mole of nucleons. 6 C 14  Answers.: Δ E = 1.02 x 10 10 kJ/mole Δ E per nucleons7.29 X 10 8 kJ/mol of nucleons

22. Nuclear Stability and the Binding Energy Binding energy per mole of nucleon measurement of nuclear stability The greater the binding energy the more difficult would be to decompose the nucleus into protons and neutrons and the more stable is the nucleus Increase of binding energy as the nucleus become heavier … containing more proton and neutrons The heavier the nuclei the more stable is the nucleons, the more they are tightly bound and give off energy if decomposed into two mid-sized nuclei. Average binding energy per nucleon increases to a maximum at mass number 50 - 60 and decreases afterwards.

23. Nuclear Binding Energies Release of the binding energy: two process occur Nuclear fission: split large nucleus into smaller ones Heavy nuclei gain stability by splitting into smaller nuclei and for high mass numbers Nuclear fusion: fuse small nuclei into larger ones Very light nuclei are combined or fused together to form more massive nuclei and for low mass numbers Both of them are EXOTHERMIC

24. Problems

25. Problems: 1. Calculate the change of energy, Δ E in kJ per gram of reactants in fusion of :

26. Problems: 2. Calculate the change of energy, Δ E in kJ per gram of reactants in fusion of :

27. Problems: 3. Plutonium-239 is used as the energy source for heart pacemakers and space probes. It decays by alpha emission. A) Calculate Δ m in grams when 1 mole of Pu-239 decays. B) How much energy Δ E in kJ is given off by the decay of 2.00 mg of Pu-239

28. Problems: 4. Sodium – 24 (atomic mass = 23.99096). One of its uses is in the detection of leaks in water pipes. A) Write a balanced nuclear reaction for the decay of Na – 24. B) Calculate Δ m in grams when 1 mole of Na-24 decays. C) How much energy in kJ is given off by the decay of 10 mg of Na - 24

29. Problems: 5. For Be – 10 , calculate A) The mass defect B) The binding energy C) Binding energy per mole of nucleons

30. Problems: 6. Which has a larger binding energy F – 19 or O – 17? Explain the stability of the nucleus.

31. Problems: 7. Calculate Δ E per mole and Δ E per gram in kJ of the reactant in A) a fusion reaction, 1 H 2 + 1 H 2  2 He 4 B) a fission reaction, 92 U 235  38 Sr 90 + 58 Ce 144 + n 1 + 4 – 1 e C) Compare the energy produced.

32. Problems: 8. Which has a larger binding energy Al – 28 or Si – 28? Explain the stability of the nucleus.

33. Problems: 9. Which has a larger binding energy Al – 28 or Si – 28?

34. Problems: 10. Calculate the fusion B -10 with an alpha particle. The products of fusion are C -13 and a proton. A) Write the nuclear reaction for this process. B) How much energy is released when 1.00 g of B – 10 is fused with an alpha particle.

35. Problems: 11. Show by calculation which process produces more energy per gram of material reacting. fission: of 92 U 235 + n 1  40 Zr 94 + 58 Ce 140 + 6 – 1 e + 2 n 1 fusion: 1 H 2 + 1 H 2  1 H 3 + 1 H 1 Nuclear masses of Ce – 140 and Zr – 94 are 139.8734 and 93.8841, respectively.

36. Problems: 12. Consider the fission reaction in which U – 235 is bombarded by neutrons . The products of bombardment are Rb – 89, Ce – 144, beta particles and more neutrons. A) Write the balanced nuclear equation for the bombardment B) Calculate Δ E when 1 gram of U – 235 undergoes fission.

37. Problems: 13. Calculate Δ E per mole and Δ E per gram in kJ of the reactant in a fusion reaction, 1 H 2 + 1 H 2  2 He 4 a fission reaction, 92 U 235  38 Sr 90 + 58 Ce 144 + n 1 + 4 – 1 e c) Compare the energy produced.

38. General information : Nuclear fission and fusion

39. Nuclear Fission Julius Robert Oppenheimer – American theoretical physicist Director of The Manhattan Project, 1938 – produced the first atomic bomb during WW II First nuclear explosion…… July 16, 1945 (when a plutonium implosion device was tested at a site located 210 miles south of Los Alamos, New Mexico on the barren plains of the Alamogordo Bombing Range, known as the Jornada del Muerto )

40. Nuclear Fission Hiroshima : August 6, 1945; “Little Boy” an  enriched uranium gun-type fission weapon Nagasaki : August 9, 1945; “Fat man” , a  plutonium   implosion-type nuclear weapon

41. Nuclear fission Nuclear fission = a nuclear reaction in which a nucleus splits into two or more smaller nuclei resulting for a lighter nuclei and a large amount of energy is released Example: 1. 92 U 235 + n 1  38 Sr 95 + 54 Xe 139 + n 1 2. Fission of uranium – 236 in neutron results in the formation two elements with mass number X – 96 and atomic number of 35 and mass number of X – 137 plus neutron 41

42. Nuclear fission During fission, the incoming neutron move slowly because it is absorbed by the nucleus, Example: The heavy 235 U nucleus can split into many different daughter nuclei, 1 n + 238 U 92  142 Ba 56 + 91 Kr 36 + 3 n 1 releases 3.5  10 11 J per 235 U nucleus.

43. Nuclear fission: theory For every 235 U fission it produces 2.4 neutrons Each neutron produced can cause the fission of another 235 U nucleus. Each neutron can cause another fission Increasing the number of fissions and the energy increase rapidly. A chain reaction forms. Consider the fission of a nucleus that results in daughter neutrons Without controls, an explosion results.

44. Nuclear fission A Nuclear Chain Reaction. The process is initiated by the collision of a single neutron with a  235 U nucleus, which undergoes fission, because each neutron released can cause the fission of another  235 U nucleus, the rate of a fission reaction accelerates geometrically. Each series of events is a generation.

45. Nuclear fission Approximate amount of radioactive element used: subcritical mass ---- (below critical mass) the neutrons escape, and no chain reaction occurs. minimum mass of fissionable material is required for a chain reaction (or neutrons escape before they cause another fission). critical mass - enough material is present for a chain reaction to occur. supercritical mass --- anything over critical mass; explosion will occur

46. Nuclear fission Critical mass chain reaction accelerates. Example: Critical mass for 235 U is about 1 kg. uses : design of a nuclear plant and nuclear bomb. Two subcritical wedges of 235 U are separated by a gun barrel. Conventional explosives are used to bring the two subcritical masses together to form one supercritical mass, which leads to a nuclear explosion.

47. Nuclear fission To control the chain reaction: the reaction can be controlled by using control rods of material which absorbs neutrons. Radioactive elements like : cadmium and boron are strong neutron absorbers and are the most common materials used in control rods. A typical neutron absorption reaction in boron is MeV is Mega electron Volt http://hyperphysics.phy-astr.gsu.edu/hbase/NucEne/control.html

48. The Fission Process Concentration of Uranium-235 : 3% to 5% U-235 Uranium-235 is 0.7% of naturally occurring uranium

49. Fission Process The first products of nuclear fission are radioactive and decay by beta emission

50. The Fission Process-summary U-235 undergoes fission Splits into two unequal fragments Releases more neutrons than are consumed Note that in the fission process, more neutrons are produced than consumed A chain reaction results Energy is released due to the conversion of mass into energy

51. Fission Process: Application Nuclear Reactors: About 20% of the electricity generated in the US comes from the fission of U-235 in nuclear reactors Tremendous amount of heat is produced, which turns water to steam and turns a turbine to produce electricity Heavy Water Reactors : using deuterium Canadian reactors (CANDU) Use D 2 O ( 2 H 2 O) as a moderator The use of D 2 O allows the use of natural uranium without enrichment Enrichment is the process of increasing the U-235 content to a few percent from 0.7% Enrichment is an expensive, technologically demanding process Done by gaseous effusion UF 6

52. Nuclear Energy and History 1970s development of nuclear reactors that can replace fossil fuels (oil, gas, coal) as the major source of electricity In France, this has indeed happened In the US, this has not happened Accident at Three Mile Island, Chernobyl, April 26, 1986 Disposal of radioactive waste

53. Pressurized Water Reactor

54. Nuclear fusion Nuclear fusion = a nuclear reaction in which two or more nuclei combine to form a heavier nucleus and a large amount of energy is released. Example: 1. 1 H 2 + 1 H 3  2 He 4 + n 1 2. Fusion of nitrogen – 15 with hydrogen – 1 resulting an element and alpha particles. 55

55. Nuclear Fusion Light isotopes such as hydrogen are unstable with respect toward fusion into heavier isotopes More energy is released in fusing light nuclei than in splitting heavy nuclei (fission) Most reactions in the Sun are fusion.

56. Nuclear fusion Fusion products are not usually radioactive, so fusion is a good energy source. Hydrogen required for reaction can easily be supplied by seawater. High energies are required to overcome repulsion between nuclei before reaction can occur. High energies are achieved by high temperatures: the reactions are thermonuclear.

57. Nuclear fusion High energies are achieved by high temperatures: the reactions are thermonuclear. Fusion of tritium and deuterium requires about 40,000,000K: 2 1 H + 3 1 H  4 2 He + 1 n These temperatures can be achieved in a nuclear bomb or a tokamak.

58. Nuclear fusion A tokamak is a magnetic bottle: strong magnetic fields contained a high temperature plasma so the plasma does not come into contact with the walls. (No known material can survive the temperatures for fusion.) To date, about 3,000,000 K has been achieved in a tokamak. A  tokamak  (Russian: Токамáк ) is a device which uses a powerful magnetic field to confine a hot plasma in the shape of a torus. The  tokamak  is one of several types of magnetic confinement devices being developed to produce controlled thermonuclear  fusion  power. Δ

59. Issues with Nuclear Fusion As an energy source, nuclear fusion has several advantages over fission Light isotopes are more abundant than heavy ones Greater energy release Non-radioactive products Disadvantages Large activation energies High temperatures are difficult to contain

60. How does a tokamak work?

61. Tokamak

62. Update of tokamak: China Fusion Engineering Testing Reactor  ( CFETR) June 1, 2021 China’s Experimental Advanced Superconducting Tokamak (EAST) fusion reactor on 28 May achieved another world record by maintaining a plasma temperature at 120 million degrees Celsius for 101 seconds and at 160 million degrees Celsius for 20 seconds, a major step toward the test run of the fusion reactor. EAST is located at the Hefei Institutes of Physical Science of the Chinese Academy of Science (ASIPP) in Hefei. It is one of three major domestic tokamaks now in operation in China. China’s HL-2M tokamak fusion reactor at CNNC’s Southwestern Institute of Physics (SWIP) in Chengdu, Sichuan was commissioned in December 2020 - an upgrade the previous model, the HL-2A. The third is J-TEXT at the Huazhong University of Science and Technology (HUST).

63. Update of tokamak: Nov. 2, 2020 The UK Atomic Energy Authority (UKAEA)'s fusion energy experiment - the Mega Amp Spherical Tokamak (MAST) Upgrade tokamak at Culham Science Centre - has achieved first plasma for the first time. MAST Upgrade will be the forerunner of the UK's prototype fusion power plant - Spherical Tokamak for Energy Production (STEP) - due for completion by 2040. It will also aid preparations for Iter - the world's largest science megaproject, under construction in the South of France, which intends to demonstrate fusion power on an industrial scale. The ITER (International Thermonuclear Experimental Reactor) project

64. Application: Nuclear Fusion and Stars

65. Application: Laser Fusion