Question

answer plz..............

Answer 1

Nucleus is initially stationary, so its speed is zero. Its momentum (p = mv) is also zero initially.

The nucleus contains an amount of A nucleons.
Nucleus decays by emitting proton with speed v to form new nucleus with speed u.
Number of nucleons in new nucleus = A – 1
Let the mass of 1 nucleon = m

After decay,
Momentum of proton = mv    {the proton is a nucleon}
Momentum of new nucleus = (A – 1)m(–u)  
{negative is taken for the speed because the new nucleus and the proton travel in opposite direction. The direction of motion of the proton is taken as positive [v is taken as positive], so u should be taken as negative.}

Total momentum after decay = mv – (A – 1)mu

From the conservation of momentum,
Sum of momentum before decay=sum of momentum after decay
0 = mv – (A – 1)mu
v = (A – 1)u