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- 39.8 An atom of uranium-235 (atomic mass: m(23U) cays to thorium-231 (atomic mass: 231. 00 Th) = 231.03630 u) emission of an 235.04392 u) de- 92 via the a particle (nuclear 4.00151 u). m(ža) c = 2.998 x 108 m s-1. mass: Use %D (a) What is the binding energy of an 235U nucleus (in J)? 92 (b) What is the binding energy of a 231 Th nucleus (in J)? 90 (c) What is the binding energy of an a particle (in J)? (d) What is the maximum possible ki- netic energy (in J) of the a particle emitted during this decay? (Hint: what is the difference between the mass of 23°U and the total mass of 92 231 Th and an a particle?) 90 (e) Whatis the maximum velocity of the emitted a particle?What minimum energy E(min) is needed to remove a neutron from K40 and so convert it to K39? The atomic masses of the two isotopes are 39.964000 and 38.963708 u, respectively. E(min) = ? eVConsider the following a-decay of the Uranium nucleus 236 U → 332Th + a. 90 (a) Show how the mass number (Aa) and atomic number (Za) of the alpha particle are obtained from this equation. (b) Calculate the Q-value (Qa) of the reaction. (c) Calculate the speed va = √2MQ of the alpha particle after it has been ejected from the parent nucleus, in terms of the speed of light c. M = -, mp and ma are the atomic masses (ma+mp) x ma mp of the daugher nucleus and the alpha particle, respectively. (d) Calculate the classical turning radius Re= 2Zpe²/Qa, where Zp is the atomic number of the daughter nucleus, and e² = 1.44 MeV. fm. (e) Calculate the decay probability Pa that the alpha particle will tunnel through the barrier. HINT: In calculating the probability, use the fact that ħc=197.327 MeV fm. The formula to use is given on page 5.
- What is the nuclear equation for 2Pu (alpha decay) wwwwwww 244PU 242 90 1) 244 Pu → 24QU + ¿He 92 248 c. 2Pu -> 94 244Pu → 246TH + ZHe 94 90(a) In addition to uranium, plutonium is also a well-suited starting product for the release of energy through nuclear fission. If you bombard a ²32Pu nucleus with a neutron the fission products 94 barium ¹Ba and strontium 3Sr are formed. 56 (i) Write down the full equation of the reaction. (ii) Calculate the reaction energy in eV units. Note that m(232Pu) = 239.052162u, 94 m(¹Ba) = 143.922955u, and m(Sr) = 93.915356u. (iii) Explain what triggers a chain reaction with 232 Pu. 94An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of 14C. Find the minimum age (in years) of the charcoal. Carbon-14 has a half-life of 5730 years which means half of it will be gone after 5730 years. You may find the equality 210 = 1024 to be useful.