A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
Initial momentum of the system before disintegration is given as,
p i = m u
Where, m is the mass of parent nucleus and u is its velocity.
By substituting the given values in the above expression, we get
p i = m × 0 = 0
Momentum of the system after disintegration is given as,
p f = m 1 v 1 + m 2 v 2
Where, m 1 and m 2 are the masses of the two daughter nuclei respectively and v 1 and v 2 are their respective velocities.
According to the law of conservation of momentum,
p i = p f
By substituting the given values in the above expression, we get
0 = m 1 v 1 + m 2 v 2 m 1 v 1 = − m 2 v 2
The negative sign indicates that the motion of two daughter nuclei is in opposite direction.
Thus, the momentum of both nuclei is equal but opposite hence, they move in opposite directions.
Initial momentum of the system before disintegration is given as,
Where,
By substituting the given values in the above expression, we get
Momentum of the system after disintegration is given as,
Where,
According to the law of conservation of momentum,
By substituting the given values in the above expression, we get
The negative sign indicates that the motion of two daughter nuclei is in opposite direction.
Thus, the momentum of both nuclei is equal but opposite hence, they move in opposite directions.
