Rutherford Scattering of an Alpha Particle

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In Rutherford scattering, the minimum distance, r_min, is determined as the sum of the radii of the two nuclei involved. The alpha particle, being a helium nucleus, has a charge represented by z1, which is confirmed to be 2. For the target nucleus, the atomic number z2 is identified as 26 for iron (Fe). Understanding these values is crucial for applying the potential energy formula in scattering calculations. Accurate identification of these parameters is essential for analyzing alpha particle interactions.
ChrisWM
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Homework Statement
What kinetic energy does an a-particle have to have in order to just come into contact with the surface of an iron nucleus in a head on collision in a scattering experiment? (You may assume the iron is fixed and remains at rest during the interaction.) For the radius of the a-particle use ra = 2.60 fm and for the iron nucleus use rFe = 4.59 fm.
Relevant Equations
k=(z1e)(z2e)/(4pi*(eo)(rmin))
I have the equation but I am unsure of what my r min would be. Is it the sum of the radii or the difference? I am also confused on what z1 would be. I am fairly sure z2 is the atomic number of Fe(26) but I am unsure of this as well.
Edit: I just read that z1 could be 2, is this correct?
 
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## r_{min} ## would be the sum of the radii, because in the potential energy formula, ## r_{min} ## is the distance between the centers of the two charged nuclei. (The alpha particle is a helium nucleus, and yes ## z_1=2 ##).
 
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Charles Link said:
## r_{min} ## would be the sum of the radii, because in the potential energy formula, ## r_{min} ## is the distance between the centers of the two charged nuclei. (The alpha particle is a helium nucleus, and yes ## z_1=2 ##).
Thank you so much!
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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