Matriculation Physics ( Nuclear Reaction )

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<p>1PHYSICS CHAPTER 14Bombardment Bombardment with energetic with energetic particlesparticlesNuclear Nuclear fusionfusionNuclear Nuclear fissionfissionCHAPTER 14: Nuclear reactionCHAPTER 14: Nuclear reaction(2 Hours)(2 Hours)Four types of Four types of nuclear reaction: nuclear reaction:is defined as a is defined as a physical process physical process in which there is a in which there is a change in identity change in identity of an atomic of an atomic nucleus nucleus.RadioactivRadioactive decaye decayPHYSICS CHAPTER 142At the end of this chapter, students should be able to: At the end of this chapter, students should be able to: State State the conservation of charge ( the conservation of charge (Z Z) and nucleon ) and nucleon number ( number (A A) in a nuclear reaction. ) in a nuclear reaction.Write and complete Write and complete the equation of nuclear reaction. the equation of nuclear reaction.Calculate Calculate the energy liberated in the process of nuclear the energy liberated in the process of nuclear reaction reaction Learning Outcome:www.kmph.matrik.edu.my/physicswww.kmph.matrik.edu.my/physics14.1 Nuclear reaction (1 hour)PHYSICS CHAPTER 14314.1.1 Conservation of nuclear reactionAny nuclear reaction must obeyed conservation laws stated below:Conservation of relativistic energy (kinetic and rest energies):Conservation of linear momentum:Conservation of angular momentum:14.1 Nuclear reactionenergy ic relativistreaction before energy ic relativistreaction after momentum linear reaction before momentum linear reaction after momentum angular reaction before momentum angular reaction after PHYSICS CHAPTER 144Conservation of charge (atomic number Z):Conservation of mass number A:However, it is very hard to obey all the conservation laws.A number massreaction before A number massreaction after Z number atomicreaction before Z number atomicreaction after Note: Note:The most important important of conservation laws conservation laws should be obeyed obeyed by every nuclear reaction are conservation of charge conservation of charge (atomic atomic number number )and of mass number mass number.PHYSICS CHAPTER 145Energy is released (liberated) in a nuclear reaction in the form of kinetic energy of the particle emitted kinetic energy of the particle emitted, the kinetic energy of kinetic energy of the daughter nucleus the daughter nucleus and the energy of the gamma-ray energy of the gamma-ray photon photon that may accompany the reaction.The energy is called the reaction OR disintegration energy (Q).It may be calculated by finding the mass defect of the reaction whereThe reaction energy Q is the energy equivalent to the mass defect m of the reaction, thus14.1.2 Reaction energy (Q)( )2 c m Q nucleus of massreaction after products defect Massnucleus of massreaction before f i m m m (14.1) (14.1)(14.2) (14.2)Speed of light in vacuum Speed of light in vacuumPHYSICS CHAPTER 146is defined as the phenomenon in which an unstable nucleus the phenomenon in which an unstable nucleus disintegrates to acquire a more stable nucleus without disintegrates to acquire a more stable nucleus without absorb an external energy absorb an external energy.The disintegration is spontaneous disintegration is spontaneous and most commonly involves the emission of an alpha particle ( OR ), a beta particle ( OR ) and gamma-ray ( OR ). It also release an energy Q known as disintegration energy disintegration energy.14.1.3 Radioactivity decayNote: Note:If the value of m m OR Q Q is positive positive, the reaction is called exothermic (exoergic) exothermic (exoergic) in which the energy released energy released in the form the kinetic energy of the product.If the value of m m OR Q Q is negative, the reaction is called endothermic (endoergic) endothermic (endoergic) in which the energy need to be energy need to be absorbed absorbed for the reaction occurred.He4200e01 PHYSICS CHAPTER 147Polonium nucleus decays by alpha emission to lead nucleus can be represented by the equation below:Calculatea. the energy Q released in MeV.b. the wavelength of the gamma-ray produced.(Given mass of Po-212, mPo=211.98885 u ; mass of Pb-208, mPb=207.97664 u and mass of particle , m=4.0026 u)Solution : Solution :Example 1 :Q + + He Pb Po422088221284Q + + He Pb Po422088221284before before decay decayafter after decay decay decay f i Z Z f i A A and PHYSICS CHAPTER 148Solution : Solution :a. The mass defect (difference) of the reaction is given by The energy released in the decay reaction can be calculated by using two method: 1 1st st method: method: f i m m m ( )m m m + Pb Po( ) 0026 . 4 97664 . 207 98885 . 211 + u 10 61 . 93 m( )( )27 310 66 . 1 10 61 . 9 mkg 10 5953 . 129 kg 10 66 1 u 127 .( )( )28 2910 00 . 3 10 5953 . 1 QJ 10 436 . 112 Q( )2c m Q in kg in kgPHYSICS CHAPTER 149Solution : Solution :a. Thus the energy released in MeV is 2 2nd nd method: method:MeV 98 . 8 Q131210 60 . 110 436 . 1 QJ 10 60 1 MeV 113 .( )2c m Q MeV 95 . 8 Q22u 1MeV/ 5 . 931ccm ]]]</p> <p>,`</p> <p>.| 2MeV/ 5 . 931 u 1 c in u in u( )223u 1MeV/ 5 . 931u 10 61 . 9 cc]]]]</p> <p>,`</p> <p>.| PHYSICS CHAPTER 1410Solution : Solution :b. The reaction energy Q is released in form of gamma-ray where its wavelength can be calculated by applying the Plancks quantum theory:QhcE Qhc ( )( )128 3410 436 . 110 00 . 3 10 63 . 6 m 10 39 . 113 Note: Note:The radioactive decay only occurred radioactive decay only occurred when the value of m m OR Q Q is positive positive.PHYSICS CHAPTER 1411A nickel-66 nucleus decays to a new nucleus by emitting a beta particle.a. Write an equation to represent the nuclear reaction.b. If the new nucleus found in part (a) has the atomic mass of 65.9284 u and the atomic mass for nickel-66 is 65.9291 u, what is the maximum kinetic energy of the emitted electron?(Given mass of electron, me =5.49 104 u and c =3.00 108 m s1) Solution : Solution :a. Nuclear reaction equation must obey the conservation of atomic number and the conservation of mass number.Example 2 :Q + + e X Ni0166296628 decay( ) Ni6628PHYSICS CHAPTER 1412Solution : Solution :b. Given The mass defect (difference) of the reaction is given by If the reaction energy is completely convert into the kinetic energy of emitted electron, therefore the maximum kinetic energy of the emitted electron is given byf i m m m ( )e X Ni m m m + ( )410 49 . 5 9284 . 65 9291 . 65 + u 10 51 . 14 mu 9284 . 65 ; u 9291 . 65X Ni m m( )( )( )28 27 410 00 . 3 10 66 . 1 10 51 . 1 J 10 26 . 214max KQ K max( )2c m PHYSICS CHAPTER 1413Table 14.1 shows the value of masses for several nuclides. Discuss whether it is possible for to emit spontaneously an alpha particle. Solution : Solution :If emits an alpha particle, the decay would be represented bySince the total mass after the reaction is greater than that before the reaction, therefore the reaction does not occur.Example 3 :Nuclide Mass (u)4.002622.989826.9815He42Al2713Na2311Table 14.1 Table 14.1Al2713Al2713Al2713Na2311 +He4226.9815 u 26.9815 u 22.9898 u 22.9898 u 4.0026 u 4.0026 u26.9924 u 26.9924 uPHYSICS CHAPTER 1414is defined as an induced nuclear reaction that does not an induced nuclear reaction that does not occur spontaneously; it is caused by a collision between a occur spontaneously; it is caused by a collision between a nucleus and an energetic particles such as proton, neutron, nucleus and an energetic particles such as proton, neutron, alpha particle or photon alpha particle or photon.Consider a bombardment reaction in which a target nucleus X is bombarded by a particle x, resulting in a daughter nucleus Y, an emitted particle y and reaction energy Q:sometimes this reaction is written in the more compact form:The calculation of reaction energy Q has been discussed in section 14.1.2.14.1.4 Bombardment with energetic particlesQ + + + Y y x X( ) Y y x, X daughter nucleus daughter nucleus target (parent) target (parent) nucleus nucleusbombarding bombarding particle particleemitted emitted particle particlePHYSICS CHAPTER 1415Examples of bombardment reaction:Q + + + H O He N1117842147 ( ) O p , N178147 Q + + + He Li n B427310105ORQ + + He 2 H Li421173 ( ) He , p Li4273 ( ) Li , n B73105 ORORA nitrogen nucleus is converted into an oxygen nucleus and a proton if it is bombarded by an alpha particle carrying certain amount of energy.a. Write down an expression for this nuclear reaction, showing the atomic number and the mass number of each nuclide and particle emitted.b. Calculate the minimum energy of the alpha particle for this reaction to take place.(Given mp=0.16735 1026 kg; m =0.66466 1026kg ; mass of nitrogen nucleus , mN=2.32530 1026 kg; mass of oxygen nucleus, mO =2.82282 1026 kg ; c =3.00 108 m s1)Example 4 :N147O178PHYSICS CHAPTER 1416Solution : Solution :a. The expression represents the nuclear reaction isb. The mass defect of the reaction is Therefore the minimum energy of the alpha particle for this reaction to take place is N147O178 + Q +H11+ He42f i m m m ( ) ( )H O He N m m m m + + kg 10 1 . 230 m( )26 2610 66466 . 0 10 32530 . 2 + ( )26 2610 16735 . 0 10 82282 . 2 + Q K min ( )2min c m K ( )( )28 3010 00 . 3 10 1 . 2 J 10 89 . 113min KPHYSICS CHAPTER 1417Exercise 14.1 :Given c =3.00 108 m s1, mn=1.00867 u, mp=1.00782 u, 1. Complete the following radioactive decay equations :a.b.c.d.e.f.[ ] He Be4284 + [ ] Ba Sr Po13956973824094 + + ( ) [ ] n 3 I U101315323692 + + [ ] e Na012911 + [ ] Sc Sc47214721 + [ ] Ca K40204019 + PHYSICS CHAPTER 1418Exercise 14.1 :2. Calculate the energy released in the alpha decay below:(Given mass of U-238, mU=238.050786 u ; mass of Th-234, mTh=234.043583 u and mass of particle , m=4.002603 u)ANS. : ANS. : 6.87 6.87 10 10 13 13 J J3. The following nuclear reaction is obtained :Determine the mass of in atomic mass unit (u).(Given the mass of nitrogen nucleus is 14.003074 u)ANS. : ANS. : 14.003872 u 14.003872 uQ + + He Th U422349023892MeV 55 . 0 H C n N1114610147 + + +C146PHYSICS CHAPTER 1419At the end of this chapter, students should be able to: At the end of this chapter, students should be able to: Distinguish Distinguish the processes of nuclear fission and the processes of nuclear fission and fusion. fusion.Explain Explain the occurrence of fission and fusion in the form the occurrence of fission and fusion in the form of graph of binding energy per nucleon. of graph of binding energy per nucleon.Explain Explain chain reaction in nuclear fission of a nuclear chain reaction in nuclear fission of a nuclear reactor. reactor.Describe Describe the process of nuclear fusion in the sun. the process of nuclear fusion in the sun.Learning Outcome:www.kmph.matrik.edu.my/physicswww.kmph.matrik.edu.my/physics14.2 Nuclear fission and fusion (1 hour)PHYSICS CHAPTER 142014.2.1 Nuclear fissionis defined as a nuclear reaction in which a heavy nucleus a nuclear reaction in which a heavy nucleus splits into two lighter nuclei that are almost equal in mass splits into two lighter nuclei that are almost equal in mass with the emission of neutrons and energy with the emission of neutrons and energy.Nuclear fission Nuclear fission releases an amount of energy that is greater greater than than the energy released in chemical reaction chemical reaction.Energy is released because the average binding energy per average binding energy per nucleon of the fission products is greater than that of the nucleon of the fission products is greater than that of the parent parent.It can be divided into two types:spontaneous fission spontaneous fission very rarely occur.induced fission induced fission bombarding a heavy nucleus with slow neutrons or thermal neutrons of low energy (about 102 eV). This type of fission is the important process in the energy production.14.2 Nuclear fission and fusionPHYSICS CHAPTER 1421n10U23692La14857Br8535U23592n10n10n10For example, consider the bombardment of by slow neutrons. One of the possible reaction isThe reaction can also be represented by the diagram in Figure 14.1.Other possible reactions are:U23592Q + + + + n 3 La Br U n U10148578535236921023592Nucleus in the excited state. Nucleus in the excited state.Figure 14.1 Figure 14.1Q + + + + n 3 Xe Sr U n U10139549438236921023592Q + + + + n 3 Ba Kr U n U10144568936236921023592PHYSICS CHAPTER 1422Most of the fission fragments (daughter nuclei) of the uranium-235 have mass numbers from 90 to 100 90 to 100 and from 135 to 145 135 to 145 as shown in Figure 14.2.Figure 14.2 Figure 14.2PHYSICS CHAPTER 1423Calculate the energy released in MeV when 20 kg of uranium-235 undergoes fission according to(Given the mass of U-235 =235.04393 u, mass of neutron =1.00867 u, mass of Kr-89 =88.91756 u, mass of Ba-144 =143.92273 u and NA =6.02 1023 mol1)Solution : Solution :The mass defect (difference) of fission reaction for one nucleus U-235 is Example 5 :Q + + + + n 3 Ba Kr n U101445689361023592f i m m m ( ) ( )n Ba Kr n U3m m m m m + + + u 1863 . 0 m( ) + 00867 . 1 04393 . 235( ) 00867 . 1 3 92273 . 143 91756 . 88 + +PHYSICS CHAPTER 1424Solution : Solution :The energy released corresponds to the mass defect of one U-235 is235 103 kg of uranium-235 contains of 6.02 1023 nuclei 20 kg of urainum-235 contains ofTherefore Energy released by 20 kg U-235( )2c m Q MeV 174 Q( )22u 1MeV/ 5 . 931u .1863 0 cc]]]]</p> <p>,`</p> <p>.|nuclei 10 12 . 525 ( )23310 02 . 610 23520</p> <p>,`</p> <p>.| ( )( ) 174 10 12 . 525 MeV 10 91 . 827 PHYSICS CHAPTER 1425A uranium-235 nucleus undergoes fission reaction by bombarding it with a slow neutron. The reaction produces a strontium-90 nucleus , a nucleus X and three fast neutrons.a. Write down the expression represents the fission reaction.b. If the energy released is 210 MeV, calculate the atomic mass of nucleus X.(Given the mass of U-235 =235.04393 u, mass of neutron =1.00867 u and mass of Sr-90 =89.90775 u)Solution : Solution :a. The expression represents the fission reaction is Example 6 :( ) Sr9038Q + + + + n 3 X Sr n U101435490381023592PHYSICS CHAPTER 1426Solution : Solution :The energy released of 210 MeV equivalent to the mass defect for U-235 isTherefore the atomic mass of the nucleus X is given by( )2c m Q u 22544 . 0 m( )22u 1MeV/ 5 . 931210 ccm]]]]</p> <p>,`</p> <p>.| f i m m m ( ) ( )n X Sr n U3m m m m m m + + + u 8934 . 142X m( ) + 00867 . 1 04393 . 235 22544 . 0( ) 00867 . 1 3 90775 . 89X + + mPHYSICS CHAPTER 1427is defined as a nuclear rea...</p>

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