A nucleus with mass number 190 initially at rest emits an alpha particle. If the Q value of the reaction is 4.5 ~MeV , the kinetic energy of the alpha particle is

Step-by-step solution

Let M be the mass of the parent nucleus, m_ be the mass of the alpha particle, and m_d be the mass of the daughter nucleus. The mass number of the parent nucleus is A = 190 . The alpha particle has a mass number of 4 , so the daughter nucleus has a mass number of A - 4 = 186 . From the conservation of linear momentum, since the parent nucleus is initially at rest, the magnitude of the momentum of the alpha particle must be equal to the magnitude of the momentum of the daughter nucleus: p_ = p_d . The kinetic energy