Physics
posted by bryce tanaka .
In a location in outer space far from all other objects, a nucleus whose mass is 3.57232e25 kg and which is initially at rest undergoes spontaneous "alpha" decay. The original nucleus disappears, and two new particles appear: a He4 nucleus of mass 6.640678e27 kg (an "alpha particle" consisting of two protons and two neutrons) and a new nucleus of mass 3.50582e25 kg. These new particles move far away from each other, because they repel each other electrically (both are positively charged).
Because the calculations involve the small difference of (comparatively) large numbers, you need to keep 7 significant figures in your calculations, and you need to use the more accurate value for the speed of light, 2.99792e8 m/s.
Choose all particles as the system.
Initial state: Original nucleus, at rest.
Final state: Alpha particle + new nucleus, far from each other.
What is the rest energy of the original nucleus? Give 7 significant figures.
What is the sum of the rest energies of the alpha particle and the new nucleus? Give 7 significant figures.

Calculate the loss of rest mass energy. That will equal the sum of the kinetic energies of the two fragments.
(delta m)*c^2 = 9.322*10^30 kg*c^2
= 8.379*10^13 J
Since the original particle was stationary, the two fragments have equal and opposite momenta.
You can use that fact and the total final kinetic energy to get the velocites of each of the two fragments. Hoever, all thay ask you to do is compute m c^2 for each partricle and compare initial and final values. That has already been done above.