The nucleus is at rest i.e. v1=0 
let mass of nucleus be M and mass of a disintegrated part be m.
so the mass of the other part is M-m.
if the two parts have velocities v' and v'' repectively , then
by Law of conservation of linear momentum, we get
Mv1 = mv' + (M-m)v''
or, v' = -{ (M-m)/m}v''
Due to positive values of M-m and m, we can conclude that v' and v'' have opposite signs , i.e. the two disintegrated parts have velocities opposite in direction .
Hence Proved