An unstable nucleus, initially at rest, decays into two spherical fragments. Fragment A has radius rA charge q

An unstable nucleus, initially at rest, decays into two spherical fragments.
Fragment A has radius rA charge qA, and rest mass mA; fragment B has
radius rB, charge qB, and rest mass mB.
a. Suppose that after the decay process fragment A has velocity vA that is small compared
with the velocity of light. Develop an expression for the kinetic energy of fragment B in terms of vA, mA, and mB.

Conservation of momentum

mA vA = mB vB

vB = (mA vA /mB )

EkB = ½ mB vB² = ½ mB (mA vA /mB ) ²

EkB = ½ [ mA² vA² / mB]