A uranium nucleus of mass 238, initially at rest, decays by emitting an alpha pa
ID: 1335107 • Letter: A
Question
A uranium nucleus of mass 238, initially at rest, decays by emitting an alpha particle of mass 4, leaving behind a thorium nucleus of mass 234. If the alpha particle goes due north, in what direction will the thorium nucleus move and why? (The masses given are in atomic mass units where the mass on one proton or neutron is 1. The mass of a proton or neutron in SI units is 1.67x10-27 kg, the latter is irrelevant to the problem.)
How many times faster will the alpha particle be moving than the thorium nucleus (what is the ratio of their speeds)?
What fraction of the total kinetic energy does the recoiling thorium nucleus carry?
Explanation / Answer
Mu = mass of uranium = 238
Mth = mass of thorium = 234
Ma = mass of alpha particle = 4
V = initial velocity of Uranium particle before decay = 0
Vfa = velocity of alpha particle after decay
Vfth = velocity of thorium particle after decay
Using conservation of momentum
Mu V = Ma Vfa + Mth Vfth
238 x 0 = 4 Vfa + 234 Vfth
Vfth = - 0.018 Vfa
hence the thorium particle moves in opposite direction of alpha particle which is south.
Vfa = - 58.5 Vfth
alpha particle moves 58.5 times faster
Total Kinetic energy = (0.5) Ma Vfa2 + (0.5) Mth Vfth2
Total Kinetic energy = (0.5) (4 (58.5 Vfth)2) + 234 Vfth2 )
Kinetic energy of thorium nucleus = (0.5) 234 Vfth2
fraction = (0.5) 234Vfth2 / ((0.5) (4 (58.5 Vfth)2) + 234 Vfth2 ))
fraction = 234 / (4 (58.5)2 + 234)
fraction = 0.0168
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