(a) In spite of our inherent interest in medical applications, perhaps the most
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Question
(a) In spite of our inherent interest in medical applications, perhaps the most important application of nuclear reactions is in electrical power production. Outline the principles of electrical power production using nuclear fission. (b) The reaction through which Hahn and Strassmann discovered fission, and the reaction on which Meitner based her analysis, was ^1_0 n + ^235_92 U rightarrow ^142_56 Ba + ^92_36 Kr + 2n + 179.4 MeV. You know that reactors produce valuable medical isotopes, and dangerous high-level isotopes. One of these Cs (Z=55). High atomic number isotopes of Cs (e.g 137, 136, ...) are beta and gamma emitters. So consider a fission reaction in which an isotope of Cs is produced. Near Cs the elements are _31 Ga, _32 Ge, _33 As, _34 Se, _35 Br, _36 Kr, _37 Rb, _38 Sr, _39 Y, _40 Zr, _41 Nb, _42 Mo, _43 Te, _44 Ru, _45 Rh, _46 Pd, _47 Ag, _48 Cd, _49 In, _50 Sn, _51 Sb, _52 Te, _53 I, _54 Xe. Assume that the fission produces 3 secondary neutrons. a) What are the fission products? b) What is the compound nucleus? c) What do you suppose are the isotopes produced? d) What is the reaction? e) How would you find the Q- value for the reaction?Explanation / Answer
(a) Power production with nuclear fission:
Every nuclear is bound by a binding energy, which is released when a nuclear is splitt into two or more daughter nuclei by hitting with some incedent particle ,e.g. neutron. In principle, fuel used in nuclear power plants is Uranium-235, which upon hitting with thermal neutron, breaks into two daughter nuclei.
In general, the neutron-induced fission reaction is the reaction, in which the incident neutron enters the heavy target nucleus (fissionable nucleus), forming a compound nucleus that is excited to such a high energy level (Eexcitation > Ecritical) that the nucleus splits into two large fission fragments. A large amount of energy is released in the form of radiation and fragment kinetic energy. Moreover and what is crucial, the fission process may produce 2, 3 or more free neutrons and these neutrons can trigger further fission and a chain reaction can take place. The chain reaction is sustained, if 1 neutron per reaction is used for further reaction. Now, the heat energy released in this chain reaction is used to heat the strem of water using it as a coolant and the heated stream produces steam which is used to run turbines for generating electricity.
(b)
a) if one of the nuclei is Cs-55 along with 3 neutron emitted, the other nucleus must have z= 92-55 = 37, hence it must be, Rb-37. so fission products are: Cs-55 and Rb-37 aong with three neutrons.
b) compound nucleus is uranium-235 nucleus, in which one neutron has entered: 236U92*. where * shows the excited state.
c) We can find the isotopes produced by supposing that Cs-55 has mass number 137 or 136.
If Cs-55 has Mass number 137, then Rb-37 will have mass number: 236 - 137 - 3 (i.e. total mass of reactantes, U-235 + 1 neutron - total mass of other products, Cs-55 , 3 netrons)
Rb-37 will have mass : 96
hence isotopes in this case will be: 137Cs55 and 96Rb37
when, Cs-55 has mass number 136, then similarly to the former case, Rb-37 mass number can be found by: 236 - 136 - 3 = 97
hence, isotopes will be: 136Cs55 and 97Rb37
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