In the α decay of uranium, , the kinetic energy of the α particle is approximately

Question

In the α decay of uranium,  , the kinetic energy of the α particle is approximately

Quizplus · Accepted Answer

In α decay, the mass number of the parent nucleus decreases by 4 and the atomic number decreases by 2. The daughter nucleus is therefore thorium-234 with atomic number 90. The difference in mass between uranium-238 and thorium-234 is the mass of the α particle, and this is converted to kinetic energy. The energy released in α decay is given by the mass difference multiplied by the speed of light squared (E=mc2). The mass difference is approximately 4 amu, or 4 × 931.5 MeV/c2, which is 3726 MeV/c2. Converting this to kinetic energy gives:

KE = (3726 MeV/c2)(c2) / 2 ≈ 1863 MeV

The kinetic energy of the α particle is therefore approximately 1.863 GeV or 1863 MeV. Converting this to MeV per nucleon (the α particle has 4 nucleons) gives:

KE/nucleon = 1863 MeV / 4 = 465.75 MeV/nucleon

This is the kinetic energy per nucleon of the α particle, which is the relevant quantity for comparing with other nuclear reactions.

In the α Decay of Uranium, , the Kinetic