Halliday, Resnick & Walker — Relativity: Problem 45

45 An alpha particle with kinetic energy 7.70 MeV collides with an $^{14}\text{N}$ nucleus at rest, and the two transform into an $^{17}\text{O}$ nucleus and a proton. The proton is emitted at $90^{\circ}$ to the direction of the incident alpha particle and has a kinetic energy of 4.44 MeV. The masses of the various particles are alpha particle, 4.002 60 u; $^{14}\text{N}$, 14.003 07 u; proton, 1.007 825 u; and $^{17}\text{O}$, 16.999 14 u. In MeV, what are (a) the kinetic energy of the oxygen nucleus and (b) the Q of the reaction? (Hint: The speeds of the particles are much less than c.)