Question

A uranium-238 nucleus at rest undergoes radioactive decay, splitting into an alpha particle (helium nucleus) with mass 6.64×10-27 kg and a thorium nucleus with mass 3.89×10-25 kg. The measured kinetic energy of the alpha particle is 6.73×10-13 J. If after the decay, the thorium nucleus is observed to move in the negative z direction. After the decay, what direction did the alpha particle move? possible answers: Positive x, Negative x, Positive y, Negative y, Positive z, Negative z. After the decay, what is the kinetic energy of the thorium nucleus?

Answer 1

(a) Since after the decay, the thorium nucleus is observed to move in the negative z direction then the alpha particle will move in positive z direction due the conservation of momentum.

(b) For find out the kinetic energy of the thorium nucleus,we have to first find out energy released in this process.

The energy released in this process is

Q = (M_U – M_Th – M_He) c²

where M_U = mass of uranium-238 nucleus = 238.050789466 u

M_Th = mass of thorium nucleus = 234.043602450 u

M_He = mass of aplha particle = 4.00260325413 u

Q = (238.05079 – 234.04363 – 4.00260) u × c²

Q= (0.00458376186 u) c²

Q= (0.00458376186 u) (931.5 MeV/u)

Q= 4.26977418189 MeV

Now kinetic energy of alpha partcle Q₁=6.73×10^-13 J =4.2005359925120 MeV

So  kinetic energy of thorium partcle Q₂=Q-Q₁ = 0.06923818937 MeV = 1.109318044116461 x 10^-14 J

(Please note that mass of U-238,He-4 & Th-234 has been taken from Nuclear data center,Japan (https://wwwndc.jaea.go.jp/NuC/) as your given data will give negative Q value which means that the reaction is not possible. )see-

M_U = mass of uranium-238 nucleus = 238.050789466 u

M_Th = mass of thorium nucleus = 3.89×10^-25 kg = 234.261296186 u

M_He = mass of aplha particle = 6.64×10^-27 kg = 3.998702 u

Q = (238.050789466-234.261296186-3.998702) u = -0.20920872 u