# Homework Help: Rutherford's Experient proved the nucleus is dense

1. Dec 2, 2015

### LotusTK

I am trying to make some "longer" notes on how the findings of Rutherfords experiment.

I have said that the nucleus was deemed to be positively charged because the alpha particles sometimes were deflected and did not continue on a straight path, and this is because of the repulsive force that the nucleus and the alpha particle feel due to them both having positive charges.

I now need to explain how the experiment proved that the nucleus is dense, and im not quite sure i am there. I think there is a pretty good explanation that includes looking at momentum, but i dont know if ive quite got it.

So far i have:

"Eventhough the gold nucleus and alpha particle both feel the same forces, the gold nucleus moves a negligible amount, and the alpha particle is deflected dramatically. This is because of the large difference in mass between the alpha particle and gold nucleus. (I then showed that gold nucleus is 49.25 times more massive than the alpha particle)"

I was thinking i could talk more about how the alpha particle loses very little velocity during the interaction between the nucleus, then somehow link that to momentum...but then they dont actually collide, and there is an external force being applied to them both (F=kQq/r^2 i think?) so im not entirely sure that i can use a momentum arguement.

What else could i add to my paragraph above?

2. Dec 2, 2015

### 24forChromium

I am not exactly sure what is the purpose of this paragraph, maybe giving a little context would be helpful. Personally, I don't see much problems with what you have written, except that you should consider the fact that the gold atoms in the foil are attached to each other via shared electron cloud, this could be partially responsible to their seemingly lack of movement after collision--the neighbouring atoms shared the impulse. Something I would add to show that the nucleus is dense is that the experiment found out how small the nucleus is, then, since removing electrons causes virtually no change in the mass of an atom, it can be conclude that the mass is concentrated in the nucleus, but I am not sure if all of the auxiliary information was available a the time of the experiment.

3. Dec 2, 2015

### Mister T

No, you're missing something. There's a clue in what you said, though, about the alpha particles being only "sometimes" deflected.

Why is it that most of them are not deflected at all?

4. Dec 3, 2015

### LotusTK

I just wanted to have an explanation as to how it is proved that the nucleus is dense, that is what i was trying to get at in my paragraph. The context is just simply the Rutherford gold leaf experiment.

The shared electrons part you mentioned is actually something i never thought of, but can understand from my limited chemistry knowledge. That point is probably beyond the syllabus i am studying (A level Physics).

I fully understand the fact that removing electrons has a negligible effect on the mass of the atom, but this doesn't take place in Rutherford's experiment so im not sure i can use it to argue that the nucleus is dense in the context of Rutherford`s experiment.

5. Dec 3, 2015

### LotusTK

Most of them continue straight through the gold leaf without being deflected, this is because the atom is mostly empty space, so the majority of alpha particles will not interact / collide with the gold nuclei.

6. Dec 3, 2015

### LotusTK

What else am i missing?

7. Dec 3, 2015

### Mister T

So, the density of something like gold is known. Density is the mass of a unit cube. If that unit cube is known to be mostly empty space, what does that tell you about the parts that aren't empty space?

A similar thing was done when the density of planet Earth was first determined. (It's volume was already known at that time, so the mass is known as soon as you determine the density, and we therefore refer to the discovery as a determination of Earth's mass and hence the value of G). If the density of the planet is significantly greater than the density of the rocks and dirt near and under the surface, what does that tell you about the planet's core?

8. Dec 3, 2015

### andrewkirk

Can I please try to clear up some of my ignorance on this point?

Why do the particles only get deflected if they 'hit' or 'almost hit' the nucleus? I was imagining the deflection happening because of electrostatic repulsion between the positive charges in nucleus and alpha particle, in which case the 'size' of the nucleus would be irrelevant.

My guess is that it's because the electrostatic force is too weak to produce a major deflection, so it's actually nuclear forces that are relevant, and for those the nuclear size comes into play because it's not a simple inverse square law of force.

Is that right, or is it something else?

Thanks

9. Dec 3, 2015

### 24forChromium

Are you suggesting that the strong interaction creates repulsive effect over some distances? I have never seen anything regarding the repulsive effect of strong interaction.

10. Dec 3, 2015

### Mister T

Most particles are not deflected because most particles don't come close enough for the deflection to be measurable. Thus at this scale the size of the nucleus is not relevant insofar as it's size needs to be determined. All that can be determined is that whatever size it has, if any, is much smaller than the spacing between nuclei. It was simply the fact that only very few alphas nearly bounced back that led to the conclusion that most of the mass had to be concentrated in small regions of space with positive charge.

In the case of the Rutherford experiment the alpha particles' distance of closest approach came nowhere near what we now know to be the size of the nucleus. Even in the case of a head-on collision the alpha particles didn't have enough kinetic energy to approach the nuclear "surface". Of course, the only reason we know that now is because more energetic alpha particles are able to get even closer.

Last edited: Dec 3, 2015
11. Dec 3, 2015

### andrewkirk

I'd say 'wondering' rather than suggesting. I don't have nearly enough confidence in my understanding of particle physics to suggest anything.

I'm trying to understand how the 'size' (which I put in inverted commas because my impression is that size at the quantum level is really just about probability densities for location) could be relevant to deflection. If the deflection is electrostatic then I can't see that size has any role, as Coulomb's law operates as if a charged particle were zero-dimensional. So I'm wondering what it is that causes the deflection.

Maybe it is electrostatic and the relevance of the nuclear radius is that it defines the region within which there is a sufficiently high probability of the alpha particle coming close enough to the point charge of a proton to experience an electrostatic force that generates a detectable deflection.

12. Dec 3, 2015

### Mister T

Certainly that's the case for the Rutherford experiment.