Finding KE of the neucleus and alpha particle A nucleus whose mass is 3.363824 T

Question

Finding KE of the neucleus and alpha particle

A nucleus whose mass is 3.363824 Times 10^-25 kg undergoes spontaneous alpha decay. The original nucleus disappears and there appear two new particles: a He-4 nucleus of mass 6.640678 Times 10^-27 kg and a new nucleus of mass 3.297318 Times 10^-25 kg. (Note that the new nucleus has less mass than the original nucleus, and it has two fewer protons and two fewer neutrons.) What is the total kinetic energy of the alpha particle and the new nucleus? Use the Conservation of Momentum in order to determine the kinetic energy of the alpha particle and the kinetic energy of the new nucleus.

Explanation / Answer

Sum of Kinetic Energy:

Total KE= 8.9174e-13

Difference in mass of the two new nucleus:

Alpha/nucleus = 0.0201396 (Alpha is this times smaller than the new nucleus)

so,

8.9174e-13=KEnuclues + 0.0201396 KEnucleus

KEnucleus=8.74135e-13

KEalpha=KEtotal - KEnucleus

KEalpha=1.7605e-14

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