Question

An atomic nucleus initially moving at 420 m/s emits an alpha particle in the direction of its velocity, and the new nucleus slows to 340 m/s. If the alpha particle has a mass of 2u and the original nucleus has a mass of 220u, what speed does the alpha particle have when it is emitted?

Answer 1

The momentum after the emission of alpha must remain the same after the emission. Since the formula is p=mv, if the mass changes, the speen must change accordingly.

Before, p=mv=420*220=92400kg.m/s

After, you have two particles. The sum of their two momentum must still be 92400kg.m/s

The remaining nucleus has a mass of 218 and a momentum of:
p=mv=218*340=74120 kg.m/s

The alpha particle has a momentum of
92400-74120=18280 kg.m/s
So you can calculate its speed with
v=p/m=18280/2=9140 m/s.
IF THE ALPHA HAD BEEN EMITTED IN THE OTHER DIRECTION, you would have needed to do a vector addition.