Taking into account the recoil (kinetic energy) of the daughter nucleus, calculate the kinetic energy K, of the alpha particle in the following decay of a 235 U nucleus at rest. 235 U 231 Th+a K₁ = MeV
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- The following reaction shows the beta decay of a °H nucleus. H- He + e +v 3 1 Determine the total energy (in kev) released in this decay. kevIn the fusion reaction H+H He + n the masses of deuteron, helium and neutron express ed in amu are 2.015, 3.017 and 1.009 respectively. If 1 kg of deuterium undergoes complete fusion, find the amount of total energy released. 1 amu = 931.5 MeV/c.Consider the following decay: 232 U → 228 Th + a . 232 U has a mass of 232.0371562 u, 228 Th has a mass of 228.0287411 u, and a has a mass of 4.002603 u. 92 90 92 90 Determine the disintegration energy (Q-value) in MeV. Q = Determine the KE of the daughter in MeV. KED = Determine the KE of the a particle in MeV & as a factor of Q. KE, = KEa = Qx Determine the speed of the a particle in terms of c. For an a particle, E. = 3.727 GeV. [NOTE: G stands for giga- which means 109 & M stands for mega- which means 10°.] Valpha = XC
- Suppose the difference in rest energy of the neutron and proton were Qn = (mn − mp)c2 = x MeV instead of Qn = 1.29MeV, with all other physical parameters unchanged. Estimate Ymax, the maximum possible mass fraction in 4He, assuming that all available neutrons are incorporated into 4He nuclei. Value: x=0.183 MeV Hint: Compare the new rest energy of the neutron to the electron and consider how that would impact the decay of neutrons. Will free neutrons decay at all in this scenario? If the neutron decay is negligible, then the ratio of protons to neutrons to protons will remain the same as it was at the time of freeze-out (for a given Qn).The rest mass of a proton is 1.0072764666 u and that of a neutron is 1.0086649158 u. The "He nucleus weighs 4.002602 u. Calculate the total binding energy of the nucleus.98/43Tc decays by emitting a 140 keV gamma ray—a highenergy photon. The mass of the nucleus is approximately 98 u. By what fraction does the mass of the nucleus decrease when the gamma ray is emitted?
- c) The equation below describes the disintegration of a polonium nucleus into a lead nucleus and an alpha-particle. During the reaction energy Q is released. 210Po → He +²02Pb+Q 84 82 Calculate the loss of energy during the reaction. The masses in the atomic mass unit u are as follows: 210 206 Po= 209.98287 u, Pb = 205.97446 u and He = 4.002604 u. 84 82 You may assume that 1u is equivalent to 931 MeV. d) The lead nucleus recoils in the opposite direction to the emitted alpha particle conserving momentum. Hence calculate: i) The ratio of the recoil nucleus and alpha particle velocities ii) The kinetic energy distribution of these products.Hand written solutions are strictly prohibited.Consider the following decay: 232 U 92 a mass of 4.002603 u. 228 Th+ a. 232 U has a mass of 232.0371562 u, 228 Th has a mass of 228.0287411 u, and a has 90 92 90 A.) Determine the disintegration energy (Q-value) in MeV. Q= B.) Determine the KE of the daughter in MeV. KED= C.) Determine the KE of the a particle in MeV & as a factor of Q. KE= KE=Qx D.) Determine the speed of the particle in terms of c. For an a particle, E = 3.727 GeV. [NOTE: G stands for giga- which means 10º & M stands for mega- which means 106.] Vα = XC
- Consider 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.A beam of 6.76 MeV protons is incident on a target of 2713Al. Those that collide produce the following reaction. p + 2713Al 2714Si +1 + n (Neutral 2714Si has mass 26.986705 u.) Ignoring any recoil of the product nucleus, determine the kinetic energy of the emerging neutrons. answer in MeVA nucleus of 238 Np captures a thermal neutron to form a nucleus of 239 Np . What is the excitation energy ( to 1 dp ) in MeV for this process ?