In a location in outer space far from all other objects, a nucleus whose mass is

Question

In a location in outer space far from all other objects, a nucleus whose mass is 3.46442e-25 kg and which is initially at rest undergoes spontaneous "alpha" decay. The original nucleus disappears, and two new particles appear: a He-4 nucleus of mass 6.640678e-27 kg (an "alpha particle" consisting of two protons and two neutrons) and a new nucleus of mass 3.397947e-25 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.
rest energy = ? J

Explanation / Answer

This looks like a multipart question where this is just the first part; we only use the first piece of information.

Rest energy is just E = mc2

= (3.46442 * 10-25 kg)(2.99792 * 108 m/s)2 = 3.1136559 * 10-8 J

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