# Question regarding Rutherford's atomic model

1. Feb 24, 2013

### daselocution

1. The problem statement, all variables and given/known data

I am basically wondering how they got to the assumption that the Ve = 2Vα. I've tried it a few times and I keep on getting that based off of their other assumptions, Ve should =0, even though I know that this cannot possibly be the case.
2. Relevant equations

Conservation of momentum: Mava = Mav'a + meve

Conservation of energy: .5Mava2 = .5Mav'a2 + .5Meve2

3. The attempt at a solution

I really don't know what to do. I've tried starting under the assumption as given that Va≈Va', which leads to getting Ve=0. I tried to do a binomial expansion using the fact that Me<<Ma, but again I got zero. I'm really not sure how to approach this. Any help would be appreciated.

2. Feb 24, 2013

### tms

It's not an assumption, it's a conclusion.

Set up the equations for an elastic collision in one dimension, then get a general solution for the final velocities of both particles. Don't put in any numbers or the like, just get a general solution. Then assume that $m_1 >> m_2$, and see what you get for $v_{2f}$.

3. Feb 27, 2013

### daselocution

Thank you very much. That makes much more sense, I'm not really sure why I didn't just do that the first time. My mistake was not solving for Valpha' in terms of the other equations. Once I realized that I had to do that, it was much clearer.