An important fusion reaction in both hydrogen bombs and controlled-fusion reactors is the “DT reaction,” in which a deuteron and a triton (nuclei of heavy hydrogen isotopes) combine to form an alpha particle and a neutron with the release of much energy. Use momentum conservation to explain why the neutron resulting from this reaction receives about 80% of the energy, while the alpha particle gets only about 20%.
ANSWER: STEP 1:- The atomic number and mass numbers of the given isotopes of hydrogen are shown below. So, the deuteron has 1 proton and 1 neutron. Where triton has 1 proton with 2 neutrons. When they combine together, they form an alpha particle and one speed moving neutron. STEP 2:- Imagine they both came with some initial velocities and get combined at some point. After the collision, the momentum should be conserved, as we are doing the experiment where no other force is present. Then one alpha particle formed and one energetic neutron which balances the nuclear reaction. Alpha particle has 2 neutrons and 2 protons. As it formed energetically it became stable but the rest of the momentum was gained by the extra neutron. As the momentum of the neutron is high, it’s velocity must be high. And we know that kinetic energy depends on the square of the velocity. So the neutron takes most of the energy from the reaction. By applying momentum and total energy conservation properly, this is the only feasible solution which works.