The first nuclear reaction ever observed (in 1919 by Ernest Rutherford) was a + 147N → p+ X.
(a) Show that the reaction product "X" must be 178O.
(b) For this reaction to take place, the α particle must come in contact with the nitrogen nucleus. Calculate the distance d between their centers when they just make contact.
(c) If the α particle and the nitrogen nucleus are initially far apart, what is the minimum value of their kinetic energy necessary to bring the two into contact? Express your answer in terms of the elementary charge e, the contact distance d, and whatever else you need.
(d) Is the total kinetic energy of the reaction products more or less than the initial kinetic energy in part (c)? Why? Calculate this kinetic energy difference.