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 3.395364e-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 3.328851 e 25 kg. These new particles move far away from each other, because they repeeach other e ectricily both are positive 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- What Is the sum of the rest energles of the alpha particle and the new nucleus? Give 7 significant figures sum of rest energies The portion of the total energy of the system contributed by rest energy:-Select- Therefore the portion of the total energy of the system contributed by kinetic energy: Select- What is the sum of the kinetic energies of the alpha particle and the new nucleus? KalphaKnew nucleus

Explanation / Answer

1) The rest energy of the initial nucleus, Eo = Mo c2 = 3.055827 x 10-8 J

2) The rest energies of the alpha particle and the daughter nucleus are

E1 = M1 c2 = 5.9766102 x 10-10 J

E2 = M2 c2 = 2.995966 x 10-8 J

Sum of the rest energies = 3.0557320 x 10-8 J

The portion of the total energy of the system contributed by rest energy: C) Decreases

Therefore the portion of the total energy of the system contributed by kinetic energy: B) Increase

3)The sum of the kinetic energies of the alpha particle and the new nucleus is the difference in the energies of the initial nucleus and the sum of the rest energies of the products formed.

K.E. = Mo c2- (M2 + M1) c2 = 9.4998 x 10-13 J

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