# Nucleus energy levels, neutron energy

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• artis
In summary, nuclei have energy levels just like electrons, which can explain phenomena such as metastable states. The release of a gamma ray after neutron capture is due to the decrease in binding energy. The energy of the emitted photon may vary depending on the isotope. The discrete energy levels of nuclei can also explain why certain isotopes only accept neutrons within a specific energy range.
artis
From what I read I see that for example a radioactive nucleus is a nucleus in an excited state and when it transitions back to it's stable state (changes from one element to another due to radioactive decay) one of the ways this happens is that the nucleus emits a energetic photon with a specific energy, so let me ask

1) Do nucleus also has determined quantum energy states much like the electrons which mean that the nucleus has distinct energy levels and can't be between two such levels but only either at one or the other much like the case with excited electrons?

I am just reading a book by Elmer E. Lewis called "Fundamentals on nuclear reactor physics"
There in the beginning is given the example where Indium captures a neutron and turns into the isotope In 117, the equation also shows that upon turning into the isotope In117 a gamma ray is released , here is my next question

2) Is the gamma ray that is released after the neutron capture corresponding to the decrease in the binding energy of the nucleus because the captured neutron made the nucleus heavier?It is further noted that Isotope In 117 decays by emitting an electron and an accompanying gamma ray and turns into Sn 117 so could we say that ,
3) the captured neutron decayed into a proton (Since Sn 117 has one less neutron yet one more proton than In117) while it decayed into a proton an electron an a gamma (photon) was emitted that also have specified energy?
4) whenever a neutron decays into a proton ,is the emitted photon always of the same energy or does it matter in what element nucleus the neutron has decayed aka lighter or heavier?And lastly for now I want to ask ,
5) Are these discrete nucleus energy levels also the reason behind why the fertile U235 only "accepts" neutrons within a specific energy range (thermal neutrons) while for example U 238 accepts mostly neutrons with higher energy but also within a limited energy range or is there something else at work or am I completely off the mark?thanks.

artis said:
1) Do nucleus also has determined quantum energy states much like the electrons which mean that the nucleus has distinct energy levels and can't be between two such levels but only either at one or the other much like the case with excited electrons?

Absolutely. Nuclei have energy levels just like electrons, which explains some odd phenomena, such as metastable states. In an extreme example, Tantalum-180m, which is just Tantalum-180 with its nucleus in a certain excited state, is prevented from transitioning very easily by some complicated quantum rules and has a half-life greater than 45 quadrillion years (45x1016). This wouldn't happen if nuclei didn't have energy states.

artis said:
2) Is the gamma ray that is released after the neutron capture corresponding to the decrease in the binding energy of the nucleus because the captured neutron made the nucleus heavier?

Let's see. Below are the masses of In-116, In-117, and a free neutron.

In-116: 107,965 MeV
In-117: 108,896 MeV
N: 939.565 MeV

In-116 + N mass = 108,904.565 MeV
Subtract In-117 Mass = 8.565 MeV

This mass difference between the In-116 + Neutron system before binding and In-117 after binding means that the In-116 nucleus needs to release 8.565 MeV of energy upon capturing a neutron. So yes, the photon is the result of the difference in binding energy between the two isotopes. Note that the binding energy of In-117 is greater than that of In-116.

artis said:
It is further noted that Isotope In 117 decays by emitting an electron and an accompanying gamma ray and turns into Sn 117 so could we say that ,
3) the captured neutron decayed into a proton (Since Sn 117 has one less neutron yet one more proton than In117) while it decayed into a proton an electron an a gamma (photon) was emitted that also have specified energy?

Good question, and one that I don't have an answer for. There will be some quantity of energy that is split between the electron and photon, but I don't know how the energy is partitioned and if it is always the same.

artis said:
4) whenever a neutron decays into a proton ,is the emitted photon always of the same energy or does it matter in what element nucleus the neutron has decayed aka lighter or heavier?

The exact energy depends on the isotope. This is because the forces inside each nucleus are different and depends upon the exact number of protons and neutrons.

artis said:
5) Are these discrete nucleus energy levels also the reason behind why the fertile U235 only "accepts" neutrons within a specific energy range (thermal neutrons) while for example U 238 accepts mostly neutrons with higher energy but also within a limited energy range or is there something else at work or am I completely off the mark?

I believe that is correct.

vanhees71
Drakkith said:
So yes, the photon is the result of the difference in binding energy between the two isotopes. Note that the binding energy of In-117 is greater than that of In-116.

But as far as I can see binding energies increase for nucleus up until about the atomic mass 100, from there on the binding energy tends to decrease as each next nucleus gets heavier, shouldn't in this case the In-117 have less binding energy than In-116 ? And the amount of binding energy that decreased expressed itself as the gamma emission of the 8.565MeV that the In-116 gave up whne it capured the neutron ?

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artis said:
But as far as I can see binding energies increase for nucleus up until about the atomic mass 100, from there on the binding energy tends to decrease as each next nucleus gets heavier, shouldn't in this case the In-117 have less binding energy than In-116 ?

That's binding energy per nucleon. Total binding energy tends to get larger as the nucleus grows.

Oh Ok , so the energy with which each particle is held in the nucleus gets smaller as they get heavier while the total energy when we sum all the individual energies of each (proton, neutron) gets larger in total?
I think I get it, so the reason why one can fission a heavy nucleus is because at some point the individual binding energies per particle get low enough that they can't hold themselves together "if the right circumstances" are met.
I assume this also explains why we can get energy from a split atom because the total binding energy per the whole nucleus is smaller for the two newly created lighter nucleus sums than it was for the single heavier nucleus
as for my questions number 3,yup I still hope for an answer to thatas for question 4, so it then follows that the energy released by a neutron that decayed into a proton is dependent on the "environment" in which it happened, what makes this difference from nuclei to nuclei even though a neutron and a proton by themselves are all the same when "viewed" outside a nucleus, is this because the forces within the nucleus like binding energy( strong nuclear force?) and others influence this transition?as for my question number 5, I really do wonder whether the mechanism behind the neutron energies that can fission either U 235 or U 233, are they to do with the quantum energy levels because if I'm not mistaken even though the possibility of a neutron with an energy that is much higher to fission these is low but it still exists so how can that then happen?

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artis said:
as for question 4, so it then follows that the energy released by a neutron that decayed into a proton is dependent on the "environment" in which it happened, what makes this difference from nuclei to nuclei even though a neutron and a proton by themselves are all the same when "viewed" outside a nucleus, is this because the forces within the nucleus like binding energy( strong nuclear force?) and others influence this transition?

Exactly. Imagine you have the nucleus of deuterium, with 1 proton and 1 neutron. The neutron simply cannot decay into a proton because of the extremely strong repulsive force that would exist between two protons. The energy required to shove two protons together is actually greater than the mass difference between a proton and a neutron, meaning that neutron decay would actually require adding energy to the nucleus.

This is also the reason that proton-proton fusion in the cores of stars takes so long on average. Two protons slamming into each other simply won't stick together because of the repulsive force between them. PP fusion relies on the weak force changing a proton into a neutron during the extremely short time the two protons are close enough together to bind.

This also explains why you can't have a stable He-2 isotope, but you can have He-3, as the addition of a single neutron adds enough attractive strong force to overcome the repulsion between the two protons.

artis said:
I assume this also explains why we can get energy from a split atom because the total binding energy per the whole nucleus is smaller for the two newly created lighter nucleus sums than it was for the single heavier nucleus

I prefer to think it as a result of a mass difference, not a difference in total binding energy. You don't usually use the total binding energy very often. Usually you deal with binding energy per nucleon or mass.

artis said:
as for my question number 5, I really do wonder whether the mechanism behind the neutron energies that can fission either U 235 or U 233, are they to do with the quantum energy levels because if I'm not mistaken even though the possibility of a neutron with an energy that is much higher to fission these is low but it still exists so how can that then happen?

Good question, but I'm afraid I don't know this top well enough to explain it. Perhaps someone else can answer that.

artis said:
3) the captured neutron decayed into a proton (Since Sn 117 has one less neutron yet one more proton than In117) while it decayed into a proton an electron an a gamma (photon) was emitted that also have specified energy?
In the following link for In-117m, you can see in the tables at the bottom that there are very specific energies for emitted electrons and photons.
http://nucleardata.nuclear.lu.se/toi/nuclide.asp?iZA=490417

artis said:
And lastly for now I want to ask ,
5) Are these discrete nucleus energy levels also the reason behind why the fertile U235 only "accepts" neutrons within a specific energy range (thermal neutrons) while for example U 238 accepts mostly neutrons with higher energy but also within a limited energy range or is there something else at work or am I completely off the mark?
I think I can help you figure this one out. Look at the decay scheme for a proton (http://nucleardata.nuclear.lu.se/toi/listnuc.asp?sql=&Z=1). How many metastable states do you find for a proton? Can you change a proton into a different isotope with a neutron?

Dr_Nate said:
I think I can help you figure this one out. Look at the decay scheme for a proton (http://nucleardata.nuclear.lu.se/toi/listnuc.asp?sql=&Z=1). How many metastable states do you find for a proton? Can you change a proton into a different isotope with a neutron?
Wrong page. "Proton" is in a link there:
http://nucleardata.nuclear.lu.se/toi/nuclide.asp?iZA=10001
Proton does not decay.
Proton actually does have excited states... not shown on the page cited. But they are not really "metastable", with width over 100 MeV. Starting with Δ+, and there are others.
Yes, you can change proton into a different isotope with a neutron, because d is bound, and even stable.

the way the question is written "can you change a proton into a different isotope with a neutron"
seems kind of weird to me because I have always thought that one element can have multiple isotopes which all share the same proton number but different neutron numbers,

can you explain what this changing proton into a different isotope is all about?

Note that a proton is an isotope, one of the several isotopes of hydrogen.

this is actually hitting on a misconception I have had for a while , Why we label Protium as an isotope instead of protium being the element and all other forms of higher neutron numbers being the isotopes of hydrogen?
Looking at Hydrogen's atomic mass which is 1 I would say that protium is what we normally refer to as Hydrogen?

@Dr_Nate when you said "change proton to a different isotope" did you mean change protium to another isotope of hydrogen?

Well I think one should be able to do this although I am not sure of the exact process of how a protium atom would capture a neutron.

@snorkack what you meant by saying "d is bound" ?

artis said:
this is actually hitting on a misconception I have had for a while , Why we label Protium as an isotope instead of protium being the element and all other forms of higher neutron numbers being the isotopes of hydrogen?
Looking at Hydrogen's atomic mass which is 1 I would say that protium is what we normally refer to as Hydrogen?
In case of Br, natural Br is under 50,7 % Br-79 and over 49,3 % Br-81
Natural Ga is 60,1 % Ga-69 and 39,9 % Ga-71
Natural Cu is 69,1 % Cu-63 and 30,9 % Cu-65
Natural Cl is 75,7 % Cl-35 and 24,3 % Cl-37
Natural B is 80,0 % B-11 and 20,0 % B-10
Natural Li is 92,4 % Li-7 and 7,6 % Li-6
Natural C is 98,9 % C-12 and 1,1 % C-13
Natural N is 99,64 % N-14 and 0,36 % N-15
Natural H is 99,989 H-1 and 0,011 % H-2
That is purely a quantitative difference not qualitative. The element is a collective for all isotopes - common, rare or unstable.
artis said:
Well I think one should be able to do this although I am not sure of the exact process of how a protium atom would capture a neutron.
Proton and neutron normally give their binding energy to one gamma ray photon, of 2,18 MeV energy. They might do other things but those are less common. Like use the energy to accelerate an electron, emit multiple photons or electron-positron pair/s.
artis said:
@snorkack what you meant by saying "d is bound" ?
It is a nucleus which does not decay by emitting one neutron in order of magnitude of 10-22 s. In other words, the neutron has binding energy, and therefore can become bound, rather than only scatter.

So we could say that H1 or protium is very likely to capture a neutron because neutron has no charge so won't be repelled meanwhile a single proton is "very lonely" and such a single proton nucleus favors a higher binding energy so accepts a neutron?

But I guess there is a balance so that in order for the nucleus to accept a neutron and still be stable the number of protons also needs to increase for multiple added neutrons because above Deuterium the next is Tritium which is not stable and decays within it's half life, so the next stable element would then be Helium and here I see 2 protons and 2 neutrons and Helium is stable having 2 neutrons while Tritium is not so the extra proton's binding energy does this stabilizing effect ?

artis said:
So we could say that H1 or protium is very likely to capture a neutron because neutron has no charge so won't be repelled meanwhile a single proton is "very lonely" and such a single proton nucleus favors a higher binding energy so accepts a neutron?
Yes. d is bound. And so is t. But you should notice that "H-4" is not bound. Neutron is not repelled electrostatically, but it does suffer Fermi repulsion and needs to have momentum in any potential hole - it cannot be caught in a hole that is too shallow.
artis said:
But I guess there is a balance so that in order for the nucleus to accept a neutron and still be stable the number of protons also needs to increase for multiple added neutrons because above Deuterium the next is Tritium which is not stable and decays within it's half life, so the next stable element would then be Helium and here I see 2 protons and 2 neutrons and Helium is stable having 2 neutrons while Tritium is not so the extra proton's binding energy does this stabilizing effect ?

"Stable" is a more complex matter than "bound".
d is bound - you need energy to break any nucleons off. (I misremembered the exact number. 2,22 rather than 2,18 MeV).
This is very weakly bound for any stable nucleus. Only Be-9 is less strongly bound.
But the reason d is "stable" is - what could it decay to?
Not p and n, that was explained with being bound.
Not dineutron or diproton. Both of those have no binding energy at all.
And not two lone protons. You do have the beta decay energy of neutron but this is only 0,78 MeV. Not enough to break apart a deuteron. To the contrary, you could react two protons with an electron to a deuteron and gain 1,44 MeV energy - a very common and never observed process. Actually, you have enough energy to react two protons into a deuteron and a positron, even more common and also never observed process.

Now compare t.
The total binding energy of t is 8,48 MeV. Since dineutron is unbound, you need all that energy to knock the proton off triton. You still need 6,26 MeV to knock off one neutron, compared to the 2,22 MeV to remove the other.
But while 3 neutrons are unbound, 2 protons and 1 neutron are bound. Not as strongly as the 2 neutrons and 1 proton of triton - but the difference, 764 keV, is slightly smaller than the 782 keV beta decay energy of neutron.
Neutron in triton decays, with lower decay energy (just 18 keV) and longer half-life (12 years) than free neutron. Triton is not unstable because it is weakly bound - triton is unstable because He-3 is barely stable enough to be more stable than triton.

Regarding the proton metastable energy levels and the capture of a neutron, I was trying to lead OP to answer his 5th question: do the metastable levels have to do with neutron capture?

## 1. What are nucleus energy levels?

Nucleus energy levels refer to the different energy states that an atomic nucleus can have. These energy levels are determined by the arrangement and movement of protons and neutrons within the nucleus.

## 2. How are nucleus energy levels determined?

Nucleus energy levels are determined by the number of protons and neutrons in the nucleus, as well as their arrangement and movement. The energy levels are also affected by the strong nuclear force, which holds the nucleus together.

## 3. What is the significance of nucleus energy levels?

The energy levels of a nucleus play a crucial role in determining the stability and properties of an atom. They also determine the types of nuclear reactions that can occur within the nucleus.

## 4. What is neutron energy?

Neutron energy refers to the kinetic energy of a neutron, which is a subatomic particle found in the nucleus of an atom. The energy of a neutron can vary depending on its speed and the energy levels of the nucleus it is a part of.

## 5. How does neutron energy affect nuclear reactions?

The energy of a neutron is a key factor in nuclear reactions, as it determines whether a reaction can occur and what type of reaction it will be. Neutrons with higher energy levels are more likely to cause nuclear reactions, while lower energy neutrons are more likely to be absorbed by the nucleus.

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