Elastic collision between alpha particle and gold Nuclei

[xoxomae]

Homework Statement

When an alpha particle collides elastically with a nucleus, the nucleus recoils. Suppose a 3.94 MeV alpha particle has a head-on elastic collision with a gold nucleus that is initially at rest. What is the kinetic energy of (a) the recoiling nucleus and (b) the rebounding alpha particle? The gold nucleus has a mass of 197 u and the alpha has a mass of 4.0 u.

Homework Equations

K1+K2=3.94MeV

The Attempt at a Solution

Since the alpha particle will momentarily stop when the repulsion between the two particles is enough to stop it, the kinetic energy from the particle will all be converted into potential energy so K1f+K2f=3.94Mev. But I'm not sure where to go from here? I feel like I'm missing something simple

 

[mfb]

You are missing conservation of momentum.

At the point where the alpha particle stops the gold nucleus is already moving, but details of the collision process are not relevant here.

 

[lychette]

as mfb hints...you need first to consider conservation of MOMENTUM to find the recoil velocities...the calculate the KEs