Determining mass in scattering process

[Pietjuh]

Suppose you have an unknown atom and you shoot an alpha particle at it in a nebula chamber. Then you measure the scattering angles of the alpha particle and the atom. You see they scatter in perpendicular directions. The problem is now to determine the mass of the unknown atom.

The first thing to come to mind is to use conservation of 4-momentum.
So p + q = p' + q'. But I'm wondering if i can determine the mass of the atom alone on the information of the scattering angle. In every attempt I make I end up with an equation that contains the energies of the particles, but I don't know them, because they weren't given in the problem. Only the angles.

Can anyone give me a hint??

 

[dextercioby]

Usually such a simple scattering problem (simple by discussing only the relativistic aspect and not the quantum one) involves dealing not only with conservation of linear momentum & energy, but also of angular momentum.

I don't think knowing the scattering angles is enough.

Daniel.

 

[jtbell]

Here are your unknowns:

energy of incoming alpha particle (you know the mass of an alpha, so this also tells you the momentum);
mass of atom (which determines its energy before the collision; momentum is zero);
energy of scattered alpha (which also tells you the momentum);
energy of recoiling atom;
momentum of recoiling atom;
scattering angle of the alpha (which also tells you the recoil angle of the atom, via the given condition);

So that's six unknowns. But you have only four equations: conservation of energy, conservation of two momentum components (since the momenta all have to lie in the same plane), and the relation between mass, energy and momentum for the recoiling atom.

Therefore, you need more information.