Which is the most stable nucleus?

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 219.962 u (unified atomic mass units) where 1 u = 1.6603 × 10e−27 kg (approximately the mass of one nucleon). The mass of a radon-216 nucleus is 215.953 u, and the mass of an alpha parti- cle is 4.00151 u. Radium has 88 protons, radon 86, and an alpha particle 2. Calculate the final kinetic energy of the alpha particle. For the moment, assume that its speed is small compared to the speed of light. Use c = 3 × 108 m/s. Answer in units of J Calculate the final kinetic energy of the radon- 216 nucleus. Answer in units of J

• Answer:

  Okay I just now figured out how to solve this. First just Subtract the mass of the alpha particle and mass of the daughter nucleus from the original mass. You'll find you lost some mass somewhere. This will be equal to the kinetic energy distributed between the alpha particle and daughter nucleus. Next you have to go to the momentum principle to get the velocities in terms of one another so you can solve. Since the initial momentum of the system has to equal the final momentum of the system, you know that P(alpha particle) + P(Radon-216) = 0 (since the intial Radium atom was at rest). From here you can discern that the magnitudes of the momentums of the alpha particle and radon atom must be equal. (MaVa = MraVra). Knowing this, you can get either of the velocities in terms of the other. I chose to divide the momentum of the Radon atom by mass of the Alpha particle. During this step, you discover that V(alpha Particle) = 53....V(Radon). Now you can plug this value into your kinetic energy equations for the two objects. (1/2*Mass*V^2). Collect your like terms by adding up the two terms (now both in terms of the velocity of Radon), and solve for V^2. Once you know what V(Radon)^2 is, you can multiply by (215.953*1.6603e-27) and divide by 2 to get the kinetic energy of Radon-216. Hope this wasnt too confusing. Your answer will come out to be 2.05480e-14 J