Energy Relations in Alpha Particle Emission

In the decay of 238U, about 77% of the alpha particles are emitted with a kinetic energy of 4.20 MeV and 23% with an energy of 4.15 MeV. For the 4.20-MeV alpha particle, which corresponds to a transition to the ground state of 234Th,

where the mass M is the atomic mass of the species in question, and Ea and ETh are the kinetic energies of the alpha particle and thorium nucleus, respectively. The 4.15-MeV alpha particle corresponds to a transition to an excited state of 234Th, with an excitation energy of 0.05 MeV. The excited state then decays to the ground state with the emission of a 0.05-MeV gamma ray.

In each case the total decay energy, summed over two successive steps in the latter case, is 4.20 MeV, plus a small additional kinetic energy of the recoiling 234Th nucleus. From conservation of momentum, when a stationary 238U nucleus decays, the momenta p of the alpha particle and of the 234Th nucleus are equal in magnitude and opposite in direction. Noting that E = p2/2M, it follows that ETh = (4/234) x Ea = 0.07 MeV. Thus the total decay energy is 4.27 MeV, as also could be found from the mass differences if numerical values are substituted in Eq. A.11.

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