# Question-Rant on Hydrogen to Helium Fusion, and Proton to Neutron Conversion

1. Jan 10, 2013

### Aspchizo

Part 1-----------------------------------------
Ok, the site I have just read through is this one. I have a few questions about it.

Firstly, about the fusion of helium into hydrogen...
http://burro.astr.cwru.edu/stu/media/fusion.jpg [Broken]

It depicts that two Protons fuse to create Deuterium which is a Proton and a Neutron, and that a by-product is a Positron. Does this actually happen?
I don't know if Wiki is reliable for this (Let me know if it's not), but apparently Electron Capture is the process in which a inner electron is pulled into the Nucleus turning one of the Protons into a Neutron.

So then under the right circumstances...

Proton + Proton = Proton + Neutron + Positron + Neutrino
and
Proton + Electron = Neutron?

So not only can a Proton be converted into a Neutron by 'absorbing(?)' a Electron, but by emitting a Positron? (Plus other stuff but i left them out for simplicity sake)

Or is there something I'm missing?

Part 2-----------------------------------------

Seems to me that there are specific masses that make stable particles, and that some particles can be combined to create different particles. The energy is conserved on both sides of the equation with the use of by products like the neutrino; low energy particle, and a photon; low energy wave. I know the gamma ray is a high energy photon, but it has a small energy level in comparison to protons, neutrons and/or electrons.

The confusing bit is how a proton turns into a neutron by emitting a positron and a neutrino.

Proton = Positron + Neutron + Neutrino

Proton + Electron = Neutron + Gamma ray

I don't know why I can't wrap my head around this. It feels like this should fit together perfectly like puzzle pieces.

The only differences between the two equations is that...
the Electron is replaced by the Positron, and thrown on the other side.
and the Neutrino is replace by a Gamma ray

Does a Gamma ray have a similar energy level to that of a Neutrino?

This turned in to a bit of a question rant, sorry for making this so long. Does anyone get what I'm trying to understand here?

Last edited by a moderator: May 6, 2017
2. Jan 11, 2013

### Staff: Mentor

Yes, it happens. One of the protons undergoes a decay via the weak force and emits a neutrino and a positron as it turns into a neutron. (To conserve charge and a few other things)

Electron capture is not the same thing. That only happens inside the nucleus of an atom, not during fusion.

Kind of. The proton-proton fusion reaction is able to turn a proton into a neutron because the end result is less massive overall than the two protons were prior to fusion. Even though a neutron has more mass than a proton, the two protons have more mass as a system when they are apart than deuterium has after fusion. This extra mass shows up as the mass of the positron and neutrino along with the kinetic energy of each reaction product. A lone proton will never turn into a neutron because it has less mass than one neutron.

Some gamma rays have more energy than the mass-energy of an electron. And some very rare gamma rays have more energy than a proton or neutron.

The particles released after decay do NOT exist inside the proton. The released particles are required because of conservation rules. For example, in the 2nd example you don't need to release a positron because charge is conserved by combining a positive and negative charge. The gamma ray is how the excess binding energy is released. In the 1st example a positron MUST be emitted in order to conserve charge. The positron is positively charged and carries the charge away.

3. Jan 11, 2013

### Aspchizo

I never ment to imply that it was, I was just musing over the nearly opposite reactions those two seemed to be. Proton releases Positron to become a Neutron, Proton absorbs Electron to become a Neutron. Idk. I was drawn to the symmetry.

Ah I was completely oblivious to the kinetic energy's contribution, can't believe I forgot about that.

Why is it that a proton and a neutron together in a nuclei are less massive than two seperate protons?

Very interesting! I never knew that.

I knew they didn't exist inside the proton. :rofl:

I'm not good with words, and I think it causes me trouble formulating concepts and such. That explanation was really good though, made a lot of sense.

So the neutrino is just a stable particle that can be created in reactions to conserve energy.
Thinking back to my previous question about why the Proton Neutron pair has less mass than two solo Protons, it probably has something to do with Binding energy?

Also...
Proton = Positron + Neutron + Neutrino
Doesn't look like it conserves mass/energy at all. This reaction must require a lot of energy? Because not only is the Neutron more massive than the proton, but it also releases a Positron and Neutrino.

Last edited: Jan 11, 2013
4. Jan 11, 2013

### snorkack

It has never been observed.
Yes. The neutrino emitted on electron capture.

For example, potassium 40 nucleus.

It has 19 protons and 21 neutrons. These are poorly bound, because odd in number. An argon 40 nucleus, with 18 protons and 22 neutrons, is much better bound. The odd proton could gain energy by somehow turning into a neutron.

There are 2 possibilities:
The proton turns into a neutron by emitting a positron (to conserve charge) but also a neutrino (to conserve spin, and also electron number). The energy left over from the binding energy of the neutron, after the higher mass of the neutron and the rest mass of the positron are satisfied, is randomly divided between positron and neutrino. The rest goes to recoil of the nucleus.
Actually, doesn´t happen. Neutrino is emitted. Usually no gamma rays.

You can have gamma rays in addition to neutrino, because you are accelerating charged particles. But this does not have to happen, and most of time does not.

Last edited by a moderator: May 6, 2017
5. Jan 11, 2013

### Staff: Mentor

Binding energy!
Yep.

No, the reaction RELEASES energy, it does not cost energy. It is actually quite rare because the proton has to decay via the weak force. This means that every time two protons slam together inside the Sun's core they only have like a one in a trillion chance of fusing. The P-P fusion chain does not happen very easily. If it did the Sun would have long run out of fuel.

6. Jan 11, 2013

### snorkack

It conserves energy - it could not happen otherwise.

It does require a lot of energy, which has to come from somewhere.

That energy may come, for example, from the binding energy of the resulting neutron.

The binding energy of neutron in deuteron actually suffices to provide the neutron and positron masses, and some of the energy is left over to be released as kinetic energies of positron and neutrino and recoil of the deuteron.

7. Jan 11, 2013

### Aspchizo

So Neutrons and Protons bound together require less energy content to be stable than a single proton proton or proton neutron pair.
That's slightly confusing, I would have thought they required more.
Can someone explain why this is?

8. Jan 11, 2013

### Staff: Mentor

It doesn't look that way to me. Considering the reaction $d \rightarrow 2n + e^+ + \nu$ and taking into account that tables of isotopic masses actually list atomic (not nuclear) masses, in order for the reaction to "go", we'd have to have

$$m_D - m_e > 2m_n + m_e \\ m_D > 2m_n + 2m_e$$

mD = 2.014102 u
mn = 1.008665 u
me = 0.000549 u

The inequality doesn't seem to be satisfied.

Last edited: Jan 11, 2013
9. Jan 11, 2013

### Staff: Mentor

Binding energy! Binding energy! Binding energy!!!

From wiki:
Binding energy is the mechanical energy required to disassemble a whole into separate parts.

Specifically for Nuclear Binding Energy:

Nuclear binding energy is the energy required to split a nucleus of an atom into its component parts. The component parts are neutrons and protons, which are collectively called nucleons. The binding energy of nuclei is always a positive number, since all nuclei require net energy to separate them into individual protons and neutrons. Thus, the mass of an atom's nucleus is always less than the sum of the individual masses of the constituent protons and neutrons when separated. This notable difference is a measure of the nuclear binding energy, which is a result of forces that hold the nucleus together. Because these forces result in the removal of energy when the nucleus is formed, and this energy has mass, mass is removed from the total mass of the original particles, and the mass is missing in the resulting nucleus. This missing mass is known as the mass defect, and represents the energy released when the nucleus is formed.

http://en.wikipedia.org/wiki/Binding_energy
http://en.wikipedia.org/wiki/Nuclear_binding_energy

One last thing. It appears as though you are thinking of this like energy is something that is needed to keep particles stable. This is not true. Energy is simply the ability to perform work. Two particles come together, fuse, and the reaction products shoot away at high velocity. This can be used to perform work on another system. So instead of saying all that we just say it releases energy.

For whatever reason heavier particles tend to decay into less massive ones UNLESS they are in a configuration where they would have less energy by remaining as they are and not decaying. This is exactly what a neutron does. Outside of a nucleus or similar environment such as a neutron star, a lone neutron decays into a proton with a half life of about 15 minutes I believe. But inside the nucleus of an atom such as deuterium the neutron stays a neutron because of the repulsive force between the two particles that would come from decaying into a proton. The nucleus as a whole is in a lower energy state than it would be if the neutron decayed into a proton.

All this energy turns out to also have mass. So measuring the mass of two protons and a deuterium nucleus would reveal that the deuterium does in fact have LESS mass than the two lone protons, even though neutrons are more massive than protons. The missing mass is taken away upon fusion by the decay products as energy or rest mass.

10. Jan 11, 2013

### Staff: Mentor

Indeed a free proton cannot decay like this, for exactly this reason.

You do get this decay for a proton that is part of certain nuclei (beta+ decay), but then what is relevant for energy conservation is not the proton and neutron masses, but rather the masses of the initial and final nuclei. If the binding energies of the two nuclei are different enough, and in the right direction, the decay can proceed.

11. Jan 11, 2013

### Staff: Mentor

I'm referring just to the P-P fusion reaction in the P-P chain in a star. Are you talking about the decay process in general?

12. Jan 11, 2013

### Staff: Mentor

Yeah, I was thinking of the decay process. Didn't read the train of thought in this thread carefully enough. For the first step in the fusion process pictured here (the p-p step):

$$2p \rightarrow d + e^+ + \nu \\ 2m_p > (m_D - m_e) + m_e \\ 2m_p > m_D$$

which works, using the following masses:

mp = 1.007276 u
mD = 2.014102 u

13. Jan 11, 2013

### Aspchizo

I know! I got that, it just doesn't make sense to me.
If a proton and electron can fuse to become a neutron (roughly) then is energy released? or is it required.
It seems analogous to the combination of two protons into a nuclei, where once becomes a neutron. Isn't that nucleus an enitrely new particle in itself then? not a combination of the two, like how a neutron isn't a proton and electron that are held together?

How do we know the proton and neutron even exist inside a nucleus?

I understand everything thus far, until the next bit.

See it seems more like the nuclei is a completely new particle instead of a cluster of particles. Why would a proton and neutron be less massive just beause they are together? Don't say "binding energy!" again because that doesn't make sense. It requires energy to break them apart, that makes sense, and it requires energy to overcome the electromagnetic force to get two protons close enough for this to happen. But being less massive together just doesn't make sense.

Mass is the Energy content of a particle (E=MC2). The energy released from these reactions is becaues of the loss of mass. The loss of mass is what doesn't make sense to me.

Right, because the gravity of a Neutron star overcomes the electromagnetic force. Is this why a Neutron can't decay inside a nuclei? because the gravitational attraction between the things in the nuclei are greater than the electromagnetic force? Clearly this must be the case because it is capable of holding electrons together. Sounds like the strong force is just gravity between extremely close particles.

Yeah, energy content = mass. I still need to wrap my head around why they have less mass. It's a big problem for me :grumpy:

As you make your way up the periodic table does the energy required to break them apart progressivley increase, and at a point begin to decrease, even to the point where it breaks itself apart?

Last edited: Jan 11, 2013
14. Jan 11, 2013

### Staff: Mentor

Without any nucleus, energy is required. In a nucleus, energy can be released (depends on the nucleus and its binding energy with proton and neutron)

A nucleus is a collection of protons and neutrons, and this collection can change the energy levels for protons and neutrons. In a similar way, a proton can change energy levels for an electron nearby - without changing any particles.

Fits perfectly to measurement results.

In a neutron star, gravity provides the attraction.
In a nucleus, the strong force provides the attraction.

No. You can calculate the gravitational force, and it is negligible. The strong force is a completely different interaction, even if it can do something similar to gravity in different setups ("hold things together").

This depends on your question: Energy per nucleus? Energy per nucleon?

15. Jan 11, 2013

### Aspchizo

Why does the particle require less energy when inside the nuclei?

Except for the change in mass?

How do we calculate this accurately? aren't we lacking a theory of quantum gravity?

The energy required to pop off one nuclei.

16. Jan 11, 2013

### Staff: Mentor

I believe they will only fuse if it provides a release of energy.

Nope. The nucleus is actually composed of separate particles. We can easily observer this by shooting electrons into the nucleus. You might be able to get away with saying the nucleus is one big composite particle much like an atom can be considered one, but that's about it.

We can shoot electrons into it, break it apart into its component particles, etc.

I think you are missing a key concept here. Potential energy. Take an electron and a proton and put them very far apart. Now let them come together until they are right on top of each other. At this point they both have lots of kinetic energy from their mutual attraction. It turns out that the mass of the proton-electron system (not atom) is equal in mass no matter if the two particles are far apart or if they are almost right on top of each other. When far apart they have lots of potential energy which is converted into kinetic energy as they accelerate and close with each other. If the proton manages to capture the electron into an orbital the kinetic energy will be released as a photon. Once this energy is radiated away the atom will have LESS mass than the two particles had before. The missing mass was radiated away as energy in the photon that was released.

No, the strong force is very very different. For one thing it doesn't decrease in strength as the distance between particles increases. This leads to something called color confinement.

http://en.wikipedia.org/wiki/Colour_confinement

The total energy does, yes. But the energy per nucleon does not. Iron and Nickel are the most tightly bound nuclei, with the greatest amount of energy per nucleon required to break them apart. This is why we cannot get energy from fusing them, and why massive stars go supernova when they build up Nickel in their core. See the chart in the Nuclear Binding Energy link.

17. Jan 11, 2013

### Staff: Mentor

We now the atomic masses, and we know the charge (Z) on the nucleus. We know that elements have isotopes, and the mass differences are nearly that mass of a free neutron, but not quite. From various measurements, we can discern the mass of nuclei, and protons, and ultimately we can determine the mass of a neutron.

We know that when a neutron is absorbed by a nucleus, the mass increases by nearly 1 amu, and some energy, equal to the binding energy is given off in the form of a prompt gamma ray. The heavier isotope, may or may not be radioactive.

We also know the above information from measurements, including nuclear scattering measurements.

We can also build models, make predictions with the models, and do experiments which do show good agreement with predictions.

So we have confidence that our understanding of nuclear structure is very good.

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/neutrondis.html
http://www-outreach.phy.cam.ac.uk/camphy/neutron/neutron4_1.htm

http://www.nobelprize.org/nobel_prizes/physics/laureates/1935/press.html

18. Jan 11, 2013

### Aspchizo

Would it be different if the nuclei were one particle? Shooting other particles at it would transfer energy and possibly allow that particle to break into seperate particles, just like how we think it knocks a proton or neutron loose. Could it or why not?

You said 'not atom', So the kinetic and potential energy of a proton-electron system change as the distance between them changes, but the mass does not change until the electron is captured by a proton. (or did I misunderstand?)
and the mass of a proton-neutron system is less when they are bound together as opposed to being seperate.

So there is a binding energy for electrons orbitting nuclei like there is for the particles contained in the nuclei?

I want to be clear that I am not doubting or challenging the theories, I am merely trying to understand them.

19. Jan 12, 2013

### Staff: Mentor

Those pieces ARE subatomic particles. Either way you look at it the math simply agrees with the nucleus being composed of small particles. Trust me, QM and QCD are FAR more accurate in their description of the nucleus than anything I could type here.

The kinetic and potential energy change as the particles get closer to each other, but they always add up to the same amount. As the velocity of each particle increases you have less potential energy and more kinetic. The sum of the two at any time during this is equal. One is merely being converted into the other.

Yes. But only AFTER they bind together and emit the extra energy as a photon or some other particle.

Yep. And there is gravitational binding energy as well.

20. Jan 13, 2013

### Staff: Mentor

Nuclei are bound systems of protons and neutrons. Atoms are bound systems of a nucleus and electrons. A neutral atom has as many electrons as protons. The number of protons in a nucleus is given by the atomic number, Z. The binding energies of nuclei are on the order of high keV or MeV, whereas electron binding energies are on the order of ev to keV. The innermost electron of the H atom has a binding energy of ~13.6 eV, while that of Lw is ~153 keV.

Molecules are bound systems of atoms. Hydrogen, oxygen and nitrogen are diatomic molecules, while the noble gases, He, Ne, Ar, Kr, Xe, Rn are naturally monatomic. Note the H, N and O like to form compounds with themselves and other elements.

I was only indicating how and when our understanding of atomic structure has developed. The understanding of nuclear structure came much later. It was in 1932 that Chadwick identified or 'discovered' the neutron - only 80 years ago.