# Homework Help: "Protons+electrons" model vs "protons+neutrons" model

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1. Nov 27, 2017

### njdevils45

1. The problem statement, all variables and given/known data
Earlier in the book it was remarked that early in the history of nuclear physics the electrically neutral mass of nuclei now attributed to neutrons was considered to arise from neutral particles composed of combinations of protons and electrons (as opposed to neutrons in their own right as fundamental particles). Here we have a look at the spin statistics of the situation. Consider a nitrogen-14 (147N) nucleus. If the "protons + electrons" model were correct , would you predict N-14 to be spin-1/2 or spin-1 system? What about in the case of the "protons + neutrons" model? Spectroscopic evidence indicates that N-14 is a spin-1 system. Which model does this support?

2. Relevant equations
Protons and electrons are both spin-1/2. Neutrons if they're fundamental particles are also spin 1/2.

3. The attempt at a solution
I said,

If a neutron were composed of protons and neutrons, then the number of protons in the neutrons would have to equal the number of electrons in order to have a neutral charge. So the neutron would have spin-1. Therefore sicne there are 7 protons, 7 neutrons and 7 electrons in our atom, the "protons + electrons" model predicts spin-1 system.

If a neutron was just fundamental with spin-1/2 then the "protons + neutrons" model predicts spin-1/2 system.

Spectroscopic evidence supports the "protons + electrons" model.

I think I have a decent understanding on what the two models are trying to say. I guess the "protons + neutrons" model is just the idea that we know today that the nucleus is made up of protons and neutrons with electrons orbiting. And I guess the "protons + electrons" model is the idea that the neutrons are made up of protons and electrons, and that the nucelus still has protons and neutrons, in addition to electrons orbiting. But shouldn't the N-14 atom have Spin-1/2 and shouldn't the "protons + neutrons" model be correct?

Last edited by a moderator: Nov 27, 2017
2. Nov 29, 2017

### Staff: Mentor

3. Nov 29, 2017

### njdevils45

I thought the model was that the neutral mass in the nucleus was composed of neutrons and that the neutrons were composed of protons and electrons. So I was thinking that the number of protons had to equal the number of neutrons in order to maintain neutrality.

4. Nov 30, 2017

### Staff: Mentor

Right. Neutrons are neutral, so they would be made out of one proton and one neutron.
That doesn't make the nucleus neutral, and it was known that nuclei are not neutral.

5. Nov 30, 2017

### njdevils45

That was a mistype.I meant to say that the number of protons should equal the number of electrons inside of the neutron. So what I'm getting now is that, a neutron, if it is composed of protons and neutrons like this model says, then it should have spin 1. Well if there's 7 spin 1/2 particles, another 7 spin 1/2, then 7 more spin 1 particles, doesn't that mean the atom is spin 1 then? I'm just confused why the book is supporting the model that seems a bit.... off. So I was thinking maybe I just misinterpreted the models themselves.

So the proton + electron model is just something that says that the neutrons are made of protons and electrons right? So shouldn't that be spin-1.

Then the proton + neutron model is just the model that we have today. And if that's 7 protons (spin 1/2) 7 electrons (spin 1/2) and 7 neutrons (spin 1/2) shouldn't the overall spin of this system be 1/2.

And also why is the Nitrogen-14 a spin 1 system? Again if it has 21 (1/2 spin) constituents, shouldn't the system be a fermion and therefore have spin-1?

6. Nov 30, 2017

### Staff: Mentor

So each neutron in carbon would have 6 electrons? That doesn't make sense.
I can't decide if the first neutron is supposed to be nucleus, or the second neutron is supposed to be electron, but I'm sure you didn't want to say neutrons are made out of protons and neutrons.
It is not. If you do the exercise properly you'll see the measurement supports that neutrons are not composed of electrons and protons.
The nucleus in the model we have today doesn't have electrons.

7. Nov 30, 2017

### Staff: Mentor

Chadwick didn't discover the neutron until 1932. As far as I know, attempted nuclear models before then didn't include a heavy neutral particle, only protons and electrons, and maybe neutrinos after Pauli proposed them in 1930. Confusingly, Pauli originally called his light neutral particle a "neutron".

I can imagine physicists saying, "Oh, this must be Pauli's neutron... no wait, it's too heavy!"

8. Nov 30, 2017

### njdevils45

WAIT A SEC!

Do these models only apply to the nucleus? I thought they were meant to apply to the entire atom. So in that case I guess it makes sense that the nucleus of the Nitrogen-14 atom does have spin-1. And that explains why the "Proton + Neutron" model is also Spin-1 and the "Proton + Electron" model is spin-1/2. Is this the case then?

9. Nov 30, 2017

### Staff: Mentor

@jtbell: It doesn't matter if you call (hypothetical) electron/proton pairs in the nucleus "neutron" or not. The important difference in allowed spin values is the same in both cases.
Sure.

10. Nov 30, 2017

### njdevils45

Oooooh okay!

That explains literally everything