What makes an atom unstable for radioactivity?

[NanakiXIII]

I've been reading about radioactivity, but I can't seem to find what actually makes an atom unstable. Can anyone tell me?

 

[vlamir]

This is very appreciable distinction, how physicists and chemists understand the word orbital.
At reading textbooks and articles by many authors-chemists each reader can find out, that chemists involuntarily (subconsciously) put the equal-sign between the words orbital and orbit of curvilinear movement.
I would like to bring for your attention some pictures, which "were drawn" with the mathematical program "MATHCAD".
During the whole year I occasionally look through these pictures and cannot understand, what benefit can be taken from these orbits and orbitals:
http://vlamir.nsk.ru/pt4_film.gif (80.5Kb)
It is the closed resonant object, which has constant length. The amplitude of oscillations cannot be more than some limit n, which in scale is shown in figure
http://vlamir.nsk.ru/pt4xn.gif (6.5Kb)
These two figures precisely correspond to experiment.
Attempts to increase amplitude of oscillations are ineffectual since for this purpose it is necessary to break off the orbit.
But the mathematical program makes it very simply.
In the following three figures the amplitude of oscillations is increased in six, twelve and twenty times, accordingly:
http://vlamir.nsk.ru/pt4x6.gif (7.5Kb)
http://vlamir.nsk.ru/pt4x12.gif (7.0Kb)
http://vlamir.nsk.ru/pt4x20.gif (6.5Kb)
With the help of the polytronic equations we can create huge set of similar projections with various number of petals, which, as you see, are similar standard orbitals. My doubts in a reality and stability of these energy states of atoms are based that for creation of these conditions the atoms or their some parts should be destroyed. On the other hand, I should trust mathematics.
I think, the imposing of resonances is the main destructive force inside atoms.

 

[Creator]

I've been reading about radioactivity, but I can't seem to find what actually makes an atom unstable. Can anyone tell me?

On a fundamental level, QED relates spontaneous decay directly to the fluctuations in the vacuum zero point field.

Creator

--"Ninety-nine percent of the lawyers give the rest a bad name".--

 

[marlon]

I've been reading about radioactivity, but I can't seem to find what actually makes an atom unstable. Can anyone tell me?

The reason is the structure of the atomic nucleus. Some nuclei contain a lot of nucleons like protons and neutrons. This requires a lot of binding energy to hold such a heavy nucleus together. Sometimes nature will find a way to make things more easy on her and thus making the nucleus lighter by reducing the number of constituent nucleons. This is the decay. You will see for example that some heavy nuclei will decay into alpha-particles (which are just Helium atoms) because they are smaller and more stable then the original bigger and unstable mother-nucleus...

This is the reason...

Another way is that due to a collision with another particle, a certain atom get's excited. Now this is a unstable state, so nature decides that the atom will undergo de-excitation in order to become a stable atom in the "rest-state". this de-excitation occurs quantummechanically by emitting photons of certain energy. Thus, electromagnetic radiation is emitted.


regards
marlon

 

[NanakiXIII]

Thanks for your replies, though I don't really understand the first. Thanks for your big reply, vlamir, but I really haven't a clue what you're talking about.

So an atom is unstable because it's big and thus harder to keep together? (I wasn't talking about colission)

But H-3 is unstable, right? But there are far bigger atoms than H-3 that are stable, aren't there?

 

[marlon]

Thanks for your replies, though I don't really understand the first. Thanks for your big reply, vlamir, but I really haven't a clue what you're talking about.

So an atom is unstable because it's big and thus harder to keep together? (I wasn't talking about colission)

But H-3 is unstable, right? But there are far bigger atoms than H-3 that are stable, aren't there?

Correct, bigger is maybe a poor choice to express myself ,

i mean this : suppose you can place 10 electrons in a row. The most stable situations are these :

1) zero electrons (ofcourse this is not very interesting...)
2) 5 electrons (just half the row filled up)
3) 10 electrons (like the elements that have the socalled octet-structure)

Now if you have 6 electrons, this is not stable and nature will try to maintain 5 electrons and lose the sixth one. That is the picture. Now, ofcourse 10 electrons is a "bigger" atom yet it is more stabile.


Keep in mind that this is just an example. If we are talking about nuclei then we need to use nucleons in stead of electrons and they are not really placed in a row. That is just for explaining it, ok ?

Also don't pay to much attention to the number 10 i use. That is just for showing you what really happens...QM can calculate the number of electrons per energy-level.


regards
marlon

 

[humanino]

The most stable of all nuclei if Fe56 :
here
For lighter nucleui, you can gain energy by fusion.
For heavier nuclei, you can gain energy by fission.

 

[humanino]

or more relevantly here

 

[humanino]

The nucleus binding is due to the residual strong interaction between quarks of different nucleons (=protons and neutrons). The nucleons exchange mesons, this results in an attractive force, usually winning against the EM repulsion between proton.

Now, what makes radioactivity ? It is the weak interaction turning one proton into one neutron, or only QM by itslef, via the tunnel effect : for instance, \alpha radiation is due to the fact that the nucleus can "see" he could gain energy, that is like falling in a potential except that there is a barrier to cross, by rearranging the nucleons in new strongly-bound states.

 

[NanakiXIII]

I meant bigger as in more protons and/or electrons in the nucleus.

I don't really understand the electron example, but...there are certain amounts of particles that are stable, while other amounts are not (or less)? Magic numbers? What exactly are Z and N? The numbers of neutrons and protons, I assume.

Thanks for your replies.

 

[humanino]

The electron orbit very far from the nucleus compared the nucleus' size ! (5 orders of magnitude) Z=number of protons
N=number of nucleons = Z+number of neutrons
Magic numbers are due to the shell strucure of the nucleus, similar to the shell structure of electrons orbits. Nucleons arrange by pairs of the same type

 

[NanakiXIII]

I see. Thanks. So why exactly are those numbers magical?

 

[marlon]

Well because these numbers correspond to the amount of nucleons that form the most stable state.

Like in the electron-example...A certain number of nucleons on one energy-level is stabile (like all possible positions filled up or just half of them)

regards
marlon

 

[NanakiXIII]

Yes, I understand that, but why do those amounts form the most stable state?

 

[humanino]

I suggest you take a look at [thread=41110]this[/thread] where the nuclear cohesion is discussed. Especially this link.

I think it is either very easy : the magic numbers account for fulfilled shell of states; or much too complicated.

 

[Chronos]

Try here for a pretty good explanation
http://www.eh.doe.gov/ohre/roadmap/achre/intro_9_2.html
In grossly simple terms, radiative emissions occur when the energies binding the atomic nucleus together are not sufficient to prevent it from falling to a lower energy state. This, in part, is why only very heavy elements are naturally radioactive.

 

[vlamir]

Nan …, for me is impressed your intense interest to the given problem. You accent the question just the one its part, which has no an exhaustive explanation.
Attempts to explain stability of ones atoms and instability of others by means of collisions are too naive for our time. More or less satisfactory explanation the energy model gives, but it cannot explain the nature of intra-atomic energy. I hope, that in the given forum participate physicists and chemists, who search for own decision of a problem, therefore I expect more original ideas.
From my side I can offer the pair of "wild" ideas, for which I cannot find mathematical interpretation.
1) The solid shell of atom is capable to focus force properties of surrounding space in the central area of atom.
2) Probably, in the nature there is an identity vacuum = time.

As to stability of hydrogen and instability of tritium (and heavier H4), this distinction can be mathematically proved by multiple increases in internal energy of atom due to multiple increases in amplitude of resonant oscillations.

 

[marlon]

Yes, I understand that, but why do those amounts form the most stable state?

Like I already said : this is because of the numbers of nucleons occupying a certain energylevel. The things I wrote in the electron-example are basic results of QM. I mean, these results are proven and that is it. Ofcourse You can keep on asking why are these results true ? However this is not how physics is done. Physics tries to describe nature, it does not tell nature how it has to work nor does it EXPLAIN why nature behaves in a certain manner...


regards
marlon

 

[humanino]

As to stability of hydrogen

The stability of the proton would have been proven ? How did you achieve that ?

 

[marlon]

Nan …, for me is impressed your intense interest to the given problem. You accent the question just the one its part, which has no an exhaustive explanation.
Attempts to explain stability of ones atoms and instability of others by means of collisions are too naive for our time. More or less satisfactory explanation the energy model gives, but it cannot explain the nature of intra-atomic energy. I hope, that in the given forum participate physicists and chemists, who search for own decision of a problem, therefore I expect more original ideas.
From my side I can offer the pair of "wild" ideas, for which I cannot find mathematical interpretation.
1) The solid shell of atom is capable to focus force properties of surrounding space in the central area of atom.
2) Probably, in the nature there is an identity vacuum = time.

As to stability of hydrogen and instability of tritium (and heavier H4), this distinction can be mathematically proved by multiple increases in internal energy of atom due to multiple increases in amplitude of resonant oscillations.

What the hell is this all about ?

And what do you mean by the stability of the proton. Are you referring to the asymptotic freedom of the strong force ?

regards
marlon

 

[NanakiXIII]

Thanks for all your replies, but so basically, they don't know?

 

[humanino]

Thanks for all your replies, but so basically, they don't know?

Yes we do know.
Did you check my link to another thread ?
In this the best known model for nucleon cohesion : Skyrme, is derived from quark/gluon level This paper is to be published soon in PRL. Is it not knowing ?

 

[NanakiXIII]

I only looked for the answer in posts after my most recent question.

Like I already said : this is because of the numbers of nucleons occupying a certain energylevel. The things I wrote in the electron-example are basic results of QM. I mean, these results are proven and that is it. Ofcourse You can keep on asking why are these results true ? However this is not how physics is done. Physics tries to describe nature, it does not tell nature how it has to work nor does it EXPLAIN why nature behaves in a certain manner...


regards
marlon

From this I derived that they didn't know.


I went back to the links you posted (that link you posted just now gets me an access denied error) and found something about closed shell configuration. I'm not sure I understand - if a shell holds a certain amount of nucleons (is full?), it's most stable?

I'm not very familiar with these shells, but they enclose each other? One thing I don't understand then, though, if I look at this image:

The red part. It looks to me like each shell needs its own amount to be full, which are equal to the magic numbers. So if the first two shells are full, it should be the most stable (for a two-shell atom), right? But Z and N wouldn't specifically be equal to the magic numbers.

 

[marlon]

Indeed we know this very well. Look, the "total" potential energy (i mean the energy off all interactions that take place inside an atom because of all kinds of interactions that are very well understood and backed up by many many experiments) of an atom with only half of the possible "nucleon-positions" filled up is lower then an atom with let's say 6 positions filled up (let's say there are maximum 10 positions to fill up in order to have a full level just like in the Aufbau-principle). A lower potential energy-state corresponds to a more stable state.

You got to compare this with the potential energy between the electron and the proton in Hydrogen. There you will also find a minimum for the potential energy of this two-body-system just when the two particles have a specific distance between them. It is at this distance that the electron orbits the proton that constitutes the nucleus of hydrogen and no other distance...


regards
marlon

 

[NanakiXIII]

Then wouldn't 0 be the most stable state and not the magical numbers? Maybe I'm confusing things now.

 

[humanino]

You are indeed confusing : link in post 8, Fe56 is the most stable configuration, for which the nucleons are the most strongly bounded together. You can also see in the "Fission and fusion can yield energy" graph, that even for light nuclei, the binding energy raises very fastly. The local maximums can also be understood in "Binding Energy for the Last Neutron as Evidence of Shell Structure" in the link of post 7.

When one shell is closed, it is not easy to take away a nucleon by striking it. It holds with his buddies together. If there is a "hole" in the structure, it gets weaker. It is the same in football I guess.

 

[reilly]

In non-relativistic QM, the process of tunneling through a potential barrier gives a very good model for radioactive decay, like alpha decay. But, in the relativistic domain, this approach was not fruitful. Rather, Fermi had the profound insight that the best he could do was to describe the beta-decay/weak interaction as a point interaction of quantum fields, suggested by the E&M interaction, -- forget the bound states, and complicated dynamics. He kept it simple, and for almost 60 years his formulation of waek interactions was IT, until suplanted by the Standard Model.


Quantum field theory is a theory of transformations: electrons change into electrons plus photons, leptons change into leptons and w-vector bosons; neutrons change into protons, electrons, and anti-neutrinos, and so on. These ideas are incorporated into field theory by means of local point interactions of quantum fields. In turn, appropriate mathematical manipulations yield interactions in terms of creation and destruction operators, as in:

(create photon)*(create electron)*(destroy electron)

or, as Fermi postulated for beta-decay

(create electron)*(create antineutrino)*(create proton)*(destroy neutron)

The process of interaction is laid out as a step-by-step process -- the picture of such a process is a Feynman diagram. The fermi interaction is represented by 4 lines radiating from a point

Here's an area where some fundamentals of QM are directly driven empirically. That is: we know atoms, nucleii and particles decay. But more generally. transformations can be seen in scattering experiments, say like photoproduction of charged pi mesons. So, in one way or another, theory must accommodate transformations among particles.

The structure of QFT interactions guarantees radioactive decays, pair production, radiation, inelastic scattering and so forth. That particles can transform is a basic assumption of QFT. Thus, we can't do much about the core why. But we can certainly describe and predict many phenomena given the QFT interactions. As always, there are three major conditions:

The mass of the decay products must be less than the mass of the parent
(Energy must be conserved along with momentum)

Angular monentum must be conserved

Selection Rules must be obeyed
(A positron cannot absorb a photon and turn into a proton;charge must
be conserved,...)

So, QFT does a great job of describing decays, but, ultimately, we really don't know quite why the decays actually happen. But then, we don't know why electric charge comes in two non-zero flavors, nor why our everyday space is 3D, nor ... Great mysteries.

Regards,
Reilly Atkinson

 

[vlamir]

Thanks Reilly!
It is the excellent analysis of the problem!

 

[NanakiXIII]

Thanks you all for trying to explain this to me, but I think I'm in over my head. I understand that a certain configuration is most stable, and if an atom isn't stable, has a not very great configuration, it decays. The rest is just a big blur of information. If Z or N or both are equal to one of the magic numbers, it's very stable, if I understand correctly. But beyond that, I'm just lost. So I think I'm just going to leave this. Maybe I'll be able to understand more in time.

But, thanks a lot anyway, I really appreciate all your help.

 

[Chronos]

Dang humanino, you give big answers to small questions. Theoretical physicists are a pain in the accelerator. Simple version [?]. Mother nature is lazy. Even a lowly atom will seek a lower energy level given the opportunity. An atom will spit out an alpha particle, beta particle or even a lousy gamma ray given the opportunity. Radioactivity is a consequence of the weak nuclear force: which is just another way of saying mother nature is lazy.

 

[geometer]

Nanaki - I've read some of the replys here and they confuse me too. First, you need to be familiar with what appears to be a basic principle of nature, and that is that nature likes to minimize potential energy (I realize guys this is oversimplified, but this is a basic explanation). Now, to radioactivity. As I am sure you're aware, the nucleus is made up of protons and neutrons. These neutrons and protons fill energy shells in the nucleus just like electrons fill energy shells around the nucleus. If some of these shells have too few or too many nucleons, the atom is not in it's most desirable energy state and acts to achieve that.

For too many neutrons, the atom converts a neutron into a proton and emits a negative particle known as a Beta-minus particle (it is essentially an electron)

For too few neutrons (in other words, too many protons), the atom converts a proton into a neutron and emits a positive particle known as a Beta-Plus particle (this is essentially an anti-electron)

For atoms that are way too big like uranium, the nucleus just spits out a chunk of itself - a particle consisting of 2 protons and 2 neutrons known as an alpha-particle.

In addition to spitting out these particles, these unstable nuclei usually emit a high frequency photon known as a gamma particle.

There are other more exotic modes of radioactive decay but these are by far the most common types encountered.

 

[geometer]

In your example of H-3, more commonly known as tritium, this is a hydrogen nucleus that contains one proton and two neutrons. A normal hydrogen nucleus is just one proton so this nucleus contains too many neutrons and it decays by Beta-Minus decay, converting one of those neutrons into a proton and emitting a Beta-Minus particle as we talked about above.

 

[marlon]

Just as a little addendum to the explanations of geometer i would like to stress the fact that the emitted electron does NOT come "out" of the nucleus. Basically, following the rules of QFT it is created out of the so called fysical vacuum (out of nothing, if you wish). The energy needed for this creation come from the decaying mother-nucleus itself via the well known formula E=mc²...

marlon

 

[vlamir]

Certainly this is very "smooth" pedantic explanation of stability and instability of isotopes, which offer geometer and marlon.
I assume, that sub-forum Theory Development should pursue other purpose – to offer an explanation for those phenomena which have no a satisfactory explanation in handbooks.
Let's look at stable and long-living isotopes of those elements, which are located before noble gases in the Periodic table:
1H (1p) – stable;
2H (1p+1n) – stable;
3H (1p+2n) – unstable: emanation of electron (beta–);

18F (9p+9n) – unstable: emanation of proton (beta+); electron capture;
19F (9p+10n) – stable;

35Cl (17p+18n) – stable;
36Cl (17p+19n) – unstable: beta+; beta–; electron capture;
37Cl (17p+20n) – stable;

77Br (35p+42n) – unstable: electron capture; beta+; gamma;
79Br (35p+44n) – stable;
81Br (35p+46n) – stable;
82Br (35p+47n) – unstable: beta+; gamma;

123I (53p+70n) – unstable: electron capture; gamma;
125I (53p+72n) – unstable: electron capture; gamma;
127I (53p+74n) – stable;
129I (53p+76n) – unstable: beta–; gamma;
131I (53p+78n) – unstable: beta–; gamma;

210At (85p+125n) – unstable: electron capture; alpha;
211At (85p+126n) – unstable: electron capture; alpha;

As you see, even this limited list of isotopes does not submit to the common rule. Especially it concerns to other isotopes (chlorine has 13 isotopes, bromine – 28, iodine – 37).
I think, there are big opportunities to explain stability and instability of isotopes due to features of a design of atoms (due to features of a geometry), but not amount of protons and neutrons in their center.