Many heavy nuclei undergo spontaneous “alpha decay,” in which the original nucleus emits an alpha particle (a helium
nucleus containing two protons and two neutrons), leaving behind a “daughter” nucleus that has two fewer protons and two
fewer neutrons than the original nucleus. Consider a radium-220 nucleus that is at rest before it decays to radon-216 by
alpha decay.
The mass of the radium-220 nucleus is 219.96274 u (unified atomic mass units) where 1 u = 1.6603 × 10−27 kg
(approximately the mass of one nucleon).
The mass of a radon-216 nucleus is 215.95308 u, and the mass of an alpha particle is 4.00151 u. Radium has 88 protons,
radon 86, and an alpha particle 2.
(a) Make a diagram of the final state of the radon-216 nucleus and the alpha particle when they are far apart, showing
the momenta of each particle to the same relative scale. Explain why you drew the lengths of the momentum vectors
the way you did.
(b) Calculate the final kinetic energy of the alpha particle. For the moment, assume that its speed is small compared to
the speed of light.
(c) Calculate the final kinetic energy of the radon-216 nucleus.
(d) Show that the nonrelativistic approximation was reasonable.