Let m = mass of the nucleus at rest.

→

u

= its initial velocity = 0 as it is at rest.
Let m1,m2 be the masses of the two smaller nuclei also called product nuclei and be their respective velocities.
If

→

p

i and

→

p

f be the initial and final momentum of the nucleus and the two nuclei respectively, then

→

p

i=m

→

u

=0...(i)

→

p

f=m1

→

v

1+m2

→

v

2...(ii)
According to the law of conservation of linear momentum,

→

p

i=

→

p

f or 0=m1

→

v

1+m2

→

v

2
or m2

→

v

2=−m1

→

v

1 or

→

v

2=−

m1 → v 1

m2

...(iii)
The negative sign in equation (iii) shows that

→

v

1 and

→

v

2 are in oppositedirections i.e. the two smaller nuclei are moved in opposite directions.