Homework Help: Scattering of Mev particles

1. Jul 25, 2011

SUDOnym

Hello
I actually wanted to posted this in the "Homework" section but it is currently working for me..

The problem is:

Calculate the cross-section for the scattering of a 10 MeV alpha particle by a gold nucleus $$_{79}^{197}Au$$ through an angle greater than (a) 10 degrees (b) 20 degrees c 30 degrees.

I know the relevant equation is:

$$\sigma=\pi(\frac{Zze^{2}}{4\pi\epsilon_{0}mv_{0}^{2}}\cot\frac{\theta}{2})^{2}$$

so its really just a plug and chug kind of problem... only thing I can't figure out is how to get the value for v_0.... i know that is hidden somewhere in the fact that it is a 10 Mev particle and I assume E=mc^2 plays a roll too.... but trying the following does not provide me with a useful value of v_o:

$$E=mc^{2}+\frac{1}{2}mv_{0}^{2}$$

neither does:

$$E=\frac{1}{2}mv_{0}^{2}$$

so my question is, how do I find the value of v_0 given that I know its an alpha particale (so I know its mass) and also that I know its 10Mev particle?

Many Thanks!

2. Jul 25, 2011

Drakkith

Staff Emeritus
What is "v_0" ?

3. Jul 25, 2011

SUDOnym

v_0 is the initial velocity that the alpha particle has before any interaction with the gold nucleus..

4. Jul 25, 2011

nasu

The correct relativistic relationship between energy and momentum is
E^2 = p^2 c^2 + m^2 c^4

Here m is the invariant mass (in the rest frame) and p =mv.
From this you can find p and then v.

5. Jul 25, 2011

SUDOnym

Thanks! to clarify though, the energy E, that I want to use will be the 10MeV...?

6. Jul 25, 2011

nasu

I think the 10 MeV should be just the kinetic energy. The rest energy of a proton is about 900 MeV so the 10 MeV cannot include the rest mass of the alpha particle.
The kinetic energy is
E^2 - m^2 c^4 = p^2 c^2

Actually at this energy the classic approximation should work quite well as KE<<E.

7. Jul 25, 2011

SUDOnym

thanks, nasu. E=1/2mv^2 was my initial try but I kept making arithmetic mistakes which is why I came on here... took me at least two hours to get the correct answer for the cross-section!

8. Jul 26, 2011

xts

Nope! Rest mass of $\alpha$-particle is 3.7GeV, so if you are speaking about 10MeV $\alpha$, it is its pure kinetic energy, and you have pretty non-relativistic case.