Heavy radioactive nucleus decay through `alpha-`decay also. Consider a radioactive nucleus x. It spontaneously undergoes decay at rest resulting in the formation of a daughter nucleus y and the emission of an `alpha-` particle. The radioactive reaction can be given by
`x rarr y + alpha`
However , the nucleus y and the `alpha-` particle will be in motion. Then a natural question arises that what provides kinetic energy to the radioactive products. In fact, the difference of masses of the decaying nucleus and the decay products provides for the energy that is shared by the daughter nucleus and the `alpha-` particle as kinetic energy . We know that Einstein's mass-energy equivalence relation `E = m c^(2)`. Let `m_(x), m_(y)` and `m_(alpha)` be the masses of the parent nucleus x, the daughter nucleus y and `alpha-` particle respectively. Also the kinetic energy of `alpha-` particle just after the decay is `E_(0)`. Assuming all motion of to be non-relativistic.
Which of the following is correct ?

Options

A. `m_(x) = m_(y) + m _(alpha)`
B. `m_(x) gt m_(y) + m _(alpha)`
C. `m_(x) lt m_(y) + m _(alpha)`
D. none of the above

Answer

D