A stationary radioactive nucleus of mass 210 units disintegrates into an alpha particle of mass 4 units and residual nucleus of mass 206 units. If the kinetic energy of the alpha particle is E, then the kinetic energy of the residual nucleus is

Options

A. `((2)/(105))E`
B. `((2)/(103))E`
C. `((103)/(105))E`
D. `((103)/(2))E`

Answer

B

Explanation

Momentum remains constant,
`K=(p^(2))/(2m)or Kprop(1)/(m)implies(K_(n))/(K_(alpha))=(m_(alpha))/(m_(n))=(4)/(206)=(2)/(103)`
`therefore` Kinetic energy of the residual nucleus
`K_(n)=((2)/(103))K_(alpha)=((2)/(103))E`