Energy in an elastic collision

[sportcardinal90]

Homework Statement

This is not really a homework problem, just me trying to get a ballpark number for a random problem.

Suppose I have a neutron flying at some energy and it hits an oxygen atom. If the oxygen atom, after the collision, now has 20 keV of energy, but before, had ~ 0, is there a way I can estimate the energy of the neutron for a range of collision angles? I do not want a precise number, but just an estimate

Homework Equations

I know some equations like conservation of energy, etc., but I am still having a hard time coming up with a ballpark solution. I tried relating the masses to the energies, but that did not seem to give a number that worked either. Neutron energy was less than oxygen energy after collision which does not make sense.[/B]

The Attempt at a Solution

 

[haruspex]

There is also conservation of momentum.
The situation has essentially two unknowns: the incoming speed of the neutron and the obliqueness of the collision. So you need two facts; the resulting energy of the oxygen atom is one, so you need one more.