Thorium 230 90Th decays to radium 22688Ra by a emission. The masses of the neutral atoms are 230.033134 u for 230 90Th and 226.025410 u for 226 88Ra. If the parent thorium nucleus is at rest, what is the kinetic energy of the emitted a particle? (Be sure to account for the recoil of the daughter nucleus.)
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Thorium 230 90Th decays to radium 22688Ra by a emission. The masses of the neutral atoms are 230.033134 u for 230 90Th and 226.025410 u for 226 88Ra. If the parent thorium nucleus is at rest, what is the kinetic energy of the emitted a particle? (Be sure to account for the recoil of the daughter nucleus.)
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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.
- 9 H the mass of the products in a fission reaction is 3.2 x 10^28 kg less than the reactants, how much energy is released in the reaction? (A) 3.6 10 45J (B) 1.1 x 10-38J (C) 9.6 x 10420 J (D) 2.9 x 10-11 JA new element has been created artificially. It is named Elementy McFacium. The most common isotope of McFacium has 153 protons and 277 neutrons. The mass of this isotope of the new element is 402,188.91 MeV/c^2. What is the total mass deficit for the nucleus? Hint: The new element is not made as an ion! Use the mass of hydrogen atoms instead of protons. (Answer in atomic mass units u)Outside the nucleus, the neutron itself is radioactive and decays into a proton, an electron, and an antineutrino. The half-life of a neutron (mass = 1.675 × 10-27 kg) outside the nucleus is 10.4 min. On average, over what distance x would a beam of 7.04-eV neutrons travel before the number of neutrons decreased to 75.0% of its initial value? Ignore relativistic effects. X = i
- The isotope of Curium 242Cm has a half-life of 160 days and emits alpha particles with an energy 6.1MeV. What is the power emitted by a sample of 242Cm with a starting number of N0 = 1018 atoms after 80 days?A 2.0-MeV neutron is emitted in a fission reactor. If it loses one-half its kinetic energy in each collision with a moderator atom, how many collisions must it undergo to reach an energy associated with a gas at a room temperature of 20.0°CWhen a nucleus decays, the daughter nucleus can be in an excited state. The 93/43Tc nucleus (molar mass 92.910 2 g/mol) in the ground state decays by electron capture and e+ emission to energy levels of the daughter (molar mass 92.906 8 g/mol in the ground state) at 2.44 MeV, 2.03 MeV, 1.48 MeV, and 1.35 MeV. (a) Identify the daughter nuclide. (b) To which of the listed levels of the daughter are electron capture and e+ decay of 93/43Tc allowed?