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Homework Help: What holds an atom together?

  1. Jul 25, 2005 #1
    I have a Mathematics teacher, who enjoys asking questions to student(s) on the subjects of Physics and Chemistry. Firstly, What holds an atom together? According to gravity, matter that orbits an object, if its terminal velocity slows down, the gravitational pull should pull the electron into the nucleus. Why isn't this the case for atoms?

    Also, I read in another discussion, (which I can't find) about the formula(s) for why electrons aren't pulled into the atom, and can freely jump to the different shelfs...

    Help! :bugeye:
     
  2. jcsd
  3. Jul 25, 2005 #2
    I can't give you a definitive answer, but I can try to point you in the right direction.

    It's generally accepted that there are four fundamental forces in the universe:
    1. Gravitational Attraction
    2. Electromagnetism
    3. Strong Nuclear Force
    4. Weak Nuclear Force

    I'm not sure how much help this will be, but maybe it'll shed some light.
     
  4. Jul 25, 2005 #3
    electrons arent pulled to the atom because of coulumb's law. but i dont know what holds atom. But before i dig information to answer this, what is the deep-ness of atom are you looking at?
     
  5. Jul 25, 2005 #4

    mukundpa

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    The -vely charged electran attracted towards positively charged nucleus but this force is not bringing it closer but utilised to rotate it round the nucleus, like a tension force is required to whirl a sone in circular path, such required force is called centripetal force and here the electric attractive force is behaving as c.p. force. Gravitationl force in this case is very very small and we are not considering it,
     
  6. Jul 26, 2005 #5
    An electrically neutral atom consists of 'electrons' and a 'nuclei consisting of nuetrons and protons'.The amount of negative charge carried by the elctrons outside the nucleus , is balanced by same amount of positive charge carried by the protons inside the nucleus.Therefore , as a whole atom is neutral.In nuetral state, atom is stable.And the electrons can be excited to higher states if sufficient energy is given to them , that is giving energy to the atom would make it unstable.Now in normal state , nucleus has a fixed '+ve charge' inside it which results in a constant force on an electron at a distance from the nucleus. This force of attraction between the nucleus and electron acts as centripetal force which acts on electron in the direction of the nucleus, as a result electron moves around in a circle.However if this centripetal force is increasing with time , the electron will accelerate while moving in circle , as a result an 'accelerating electron emits radiation' , and as it emits radiation loses energy and goes in a spiral path toward sthe nucleus, but this does not happen , because Bohr placed the electrons in energy-stable shells (like you study n=1,2 .. for hydrogen).

    There is one more theoretical reason why an electron cannot fall into the nucleus.As per Heisenberg's Uncertainity Principle, if an electron is found to be insid ethe nucleus , this means we are accurately knowing its position , this would result in tremendous gain in momentum for electron and it would shoot itself out of the nucleus.

    BJ
     
  7. Jul 26, 2005 #6
    If you are talking about the nucleus of the atom, then the strong and weak nuclear forces keep things in place. In larger atoms with more protons, the neutrons provide some displacement between the atoms so that thier electrical charges do not cause the protons in the nucleus to split into multiple nuclei. If this occured naturally fission would be happening all over the place. I guess it'd be a great source of power but first you'd have to stop everything from getting blown up. Anyways if your diving deeper into the question as what holds a proton together, well then you've got me. I know these sub atom "particles" are composed of even smaller things called quarks. In specific I believe a proton is classified as a baryon meaning its composed of 3 quarks. I think it is made of two up quarks and 1 down quark. Each up quark has a charge of +2/3 and the down quark has a charge of -1/3, so the total charge adds up to +1 (no suprise). There are 4 other "flavor" of quarks. They are called strange, charm, top, bottom, and the two mentioned - up and down. There are other physical aspects of quarks such as "color" charge as opposed to electrical charge only. While quarks establish a nice basis for particles, I believe if you keep breaking these even smaller particles down, you will keep ending up with more and more particles. Think of these things as a tournament layout. An atom as the champion, the neutron, proton, and electron in the finals bracket. Perhaps quarks in the semi-final bracket and so on. The more fundamental we try to get, the more complicated things become as we need to add dimensions onto physical quantities to remain consistent. I believe no such thing as a discrete particle exists. I think everything even at the quantum level is composed of field interactions. It would seem to me that in order to be consistent with the notion of continuity, that it is not possible to instantly go from white to black. Meaning, the boundary between two infinitely small points can be split into even a smaller jump over which there has to be a "grey" zone.
     
  8. Jul 26, 2005 #7
    To add more, there are certain 'allowed' orbits for electrons such that angular momentum of electron in these orbits is integral multiple of h/2(pie) . In these permitted orbits , even if electrons accelerate donot radiate EM Energy , but they do radiate radiations when they jump from one shell to another.

    BJ
     
  9. Jul 26, 2005 #8

    Danger

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    In the nucleus of an atom, the 'strong' nuclear force holds the protons and neutrons together. The 'weak' force is responsible for radioactive decay.
    When it comes to electrons, they are first off to be considered as noncorporeal negative charges as opposed to particles. Electron 'orbitals' define the area in which the quantum fluctuations regarded as 'electrons' are most likely to be found. Even given the ambiguity of their physical status, electrons are restricted to particular orbital distances dependent upon their energy. The change from one orbital to the next involves the absorbtion or ejection of a photon corresponding to the energy differential between the 2 orbitals.
    On this scale, gravity is totally inconsequential. And incidentally, 'terminal velocity' refers to the point at which opposing forces such as air resistance balance out gravity in a free-falling body. It has no proper usage in nuclear physics.
     
  10. Jul 26, 2005 #9
    I don't think this is correct. Heisenberg's Uncertainty Principle formulates a fundamental relation for measuring, it shows with what degree of uncertainty one can measure. The product of the uncertainty in position and the uncertainty in momentum have to be equal or higher than a certain constant. That means that if you accurately know the position of an electron you inaccurately know its momentum. There is however no "gain in momentum" (as you stated). Just because you know the position of an electron (for example) very well that doesn't mean it picks up speed or gets more massive. Correct me if I'm wrong.

    Well, you're implying there that the electron loses speed: why is that?
    The thing is that in the classical theory an accelerated electron emits photons and thereby loses energy (and therefore speed). The motion of an electron in an atom is an accelerated motion, because it's circular. Therefore, the classical theory states that the electron should "fall" into the nucleus. As we all know, there is a better theory for very small things, the quantum theory. Electrons, neutrons and protons are quantum objects. This means that they can behave wave-like and particle-like.
    The real "surprise" now is not only the way the electrons stay "in orbit" (these orbital lines are a visualization and should not be thought of as what the electrons do; it's just a model), but also the way the nucleus holds together. The nucleus of an atom is very, very small compared to the size of the atom. There's a tremendous charge density inside the nucleus in comparison to the rest. Now, the electrostatic forces should force the protons to leave the nucleus in different directions, but that doen't usually happen (fortunately) so there are other forces that hold the nucleus together: the nuclear forces (they have been mentioned). These forces act only on very small distances (electrostatic forces theoretically have an infinite reach), but in many cases it's enough to compensate for the electrostatic ones and hold the nucleus together. In some other cases it isn't: Consider an atom with many nuclear particles, many protons. They all repell each other over a distance of several protons, that means that they don't only repell their direct neighbours. The nuclear forces can't reach that far and so what happens is called a decay: the nucleus can't be kept together and the atom either emits some particles or splits up.
    For all these phenomena the effects from the electron clouds (the electron orbitals) are neglectable. The gravitational model for the electrons going around the nucleus like the earth around the sun just can't explain it all anymore.
     
  11. Jul 26, 2005 #10

    "What keep an electron form falling in? . This principle: If they were in the nucleus, we would know their position precisely, and the uncertainity principle would then require that they have a large momentum , i.e instantly gaining a very high kinetic energy.With this energy , they would break away from the nucleus.They make a compromise: they leave themselves a little room for this uncertainity and then jiggle with certain amount of motion"


    -Richard P Feynman
     
  12. Jul 26, 2005 #11
    As per modern QM , electron is no more a dot of mass , rather its a cloud and electron can be found in this cloud. These clouds have a random presence all over the atom and confining them to a finite boundary of a nucleus is precisely knowing position of electron in this cloud, not allowed.
     
  13. Jul 26, 2005 #12
    Not so sure. Any particle's uncertainty in momentum would, I assume, include 0 momentum. As the uncertainty in momentum increases, the most likely range will also shift higher up (think of a bell curve being stretched as an analogy). If you take the most likely momentum as being as good an estimate of actual momentum as we can have, this value would presumably increase as certainty in position increases.

    I asked a question on this a while back. If you have an electron at a given distance r (ignore uncertainty for now) from the nucleus then that electron has a certain potential. As the distance decreases, the potential decreases and so the momentum increases. The total of kinetic and potential energy will presumably remain the same (pending emission of photon energy). When you take into account that photons of strict energies only may be emitted, so an electron cannot radiate it's kinetic energy all the way down to the nucleus, it makes perfect sense that an electron in the nucleus will have enough momentum to escape the nucleus, otherwise it would never have been elsewhere. I didn't get any response from this, so thoughts here would be welcome.
     
  14. Jul 26, 2005 #13
    This was the quote I started a thread about, and it seemed an awful lot of people didn't take everything within it quite seriously. For instance, we would not know the precise position of the electron in a nucleus if we did not know the precise position of the nucleus itself. Secondly, as pointed out earlier, a high uncertainty in momentum does not necessitate a high momentum, only a more likely high momentum. Thirdly, none of it stops an electron 'falling in' (to my knowledge)... only from keeping it in. All of which confused me greatly until various PF members set me on the right track.
     
  15. Jul 26, 2005 #14

    ZapperZ

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    But don't you see that there is a major problem with what you are quoting from Feynman?

    You are saying that we cannot confine an electron (or anything else for that matter) with the size of a nucleus because the confinment size is too small so much so that it will have an uncertainty in momentum that is very large. Fine, let's go with that.

    However, look at the protons and neutrons themselves! They ARE confined to a spatial size THAT small! How come they don't fly off?

    The problem in quoting someone without understand the PRINCIPLE that is being illustrated is that you only see the tail end of the animal without seeing what the whole animal looks like. The uncertainty principle, DISPITE its name, is NOT a principle, but rather a CONSEQUENCE. If you solve a simple 3D coulombic potential, the LOWEST ground state energy wavefunction will produce EXACTLY the condition that is described by the uncertainty relations. You can obtain this even if you are ignorant of the HUP. It just drops onto your lap when you solve for it. It means that with JUST the coulombic potential ALONE, you have reached the limit to how small you can confine the electrons IF you care to look at it from the HUP point of view. But again, even if you're ignorant of the HUP, the solution you got already tells you that there's NO LOWER ground state than what you already have without having to invoke the HUP.

    So what's going on with the protons and neutrons? Why are they able to be confined to a region that an electron can't? If you simply apply the HUP principle here, you'll run into trouble because it is already contradictory. So the answer has to be to go back to the very beginning and look at the Hamiltonian/Schrodinger equation to be solved. Here, the potential term isn't just simply coulombic, but contains the strong interactions. This then modifies the potential well that produces the bound state and you have to re-solve the "wavefunction" all over again. This will then produces a NEW ground state, etc etc...

    Be very careful when you apply something without knowing what's under the covers.

    Zz.
     
  16. Jul 26, 2005 #15
    if speed=duck is able to quote zapper z during class, i think his math teacher will be most impressed. :tongue:
     
  17. Jul 26, 2005 #16
    Well yet again i get to an intresting thread late! So i`m going to give my 2cents worth any way even if the question has been answered

    I think the question that TheSpeed=DUCK asked is answered by Bohrs Postulate.

    Neils Bohr in 1913 postulated that the angular momentum of an orbiting electron was equactly ballanced my the electrical attraction between the positvely charged nucleus and the negative charge on an electron!

    Now remember that the copenhagen interpritation of Quantum mechanics hadn`t been suggested at this time so Bohr only had Classical mechanics and the feild equations of Maxwell to work with.

    Oh and his postulate only really works for a Hydrogen atom (when you start adding more than one electron the interactions become more complexe as there is replultion between the electrons as well as the attractive force of the nulceus!

    so her goes :

    You first need to understand the nature of the attractive force between charged particles this is refered to as the coloumb force [im not going to derive it for you now (unless you really want me to! :uhh: )] but it basiclly states that the closer two charge particles get the greater the magnitude of the force!

    Next, gravity doesn`t play a part in why the electron stays bound, gravity is a very pathetic force!, yes it its responcible of such weird things like black holes, that swallow entire star systems, but if you try you can create of force greater that the gravitational attraction of the WHOLE EARTH, try it, see how hight you can jump! by the fact that you can prooves just how weak the force is!

    Anyway i digresss, the angular momentum of an orbiting electron, should if there were no other forces present throw the electron out of it`s orbit, but it doesn't, so the attractive electrical force and the angular momentum are some how balance, basiclly there is a relativly short sequence of equations that prooves the electrons can only exist at certain distances from the nulceus.
     
  18. Jul 26, 2005 #17
    Zz I am an undergraduate and would want you to correct my misconcept(s).

    According to HUP [itex]\Delta x.\Delta p \geqq \frac{h}{4 \pi} [/itex]. Pluging in values where [itex]\Delta x[/itex] will be the size of the nucleus, we get
    [itex]\Delta v[/itex] greater than c ! We should not have velocities above c while here even the uncertainity in velocity is greater than c which indicates that our [itex]\Delta x[/itex] is incorrect ==> e- can't be confined to the nucleus.
    As the neutrons and protons differ in mass by about 10e3 the [itex]\Delta v[/itex] for n/p doesnt come above c ! So they may exist inside the nucleus.
     
    Last edited: Jul 26, 2005
  19. Jul 26, 2005 #18

    OlderDan

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    I'm long removed from the days of thinking about quantum philosophy, but at the risk of sticking my neck into a place where I might get it cut off, I gotta say I've never heard such an argument, and it strikes me has having no validity. Where does this heirarchical view of the wavefunction come from? It certainly does not come from Mr. Heisenberg who once wrote

    The more I think about the physical portion of Schrödinger's theory, the more repulsive I find it...What Schrödinger writes about the visualizability of his theory 'is probably not quite right,' in other words it's crap.

    --Heisenberg, writing to Pauli, 1926


    http://www.aip.org/history/heisenberg/p08.htm

    If wave mechanics led to some conclusion that was inconsistent with HUP, it is very likely that we would all be doing only matrix mechanics today to deal with quantum phenomena. I don't see any basis for a "chicken and egg" debate in the realm of HUP and wave mechanics. The mutual consitency of the two is why they have both survived.

    You seem to have overlooked or dismissed a fundamental difference between electrons and nucleons when you stated

    You are saying that we cannot confine an electron (or anything else for that matter) with the size of a nucleus.

    Who said that? The parenthetical addition does not come from Feynman's quote, and it is, to the best of my understanding, an erroneous extension of what he said. Momentum is the product of mass times velocity. The implications of momentum uncertainty as it relates to particle "confinement" are vastly different for two particles with a mass ratio of over 1800. Are you saying that the wave function for a nucleon in a nucleus violates the HUP?
     
  20. Jul 26, 2005 #19
    Well, I don't know in which context Feynman mentioned this, but couldn't one think of the problem like this: If you know the position of the electron very well (in the nucleus for example), the uncertainty in speed (momentum) is very high (so far we all agree, I suppose...). Now if the uncertainty in the measurement of speed is very high, that means we're not able to say anything precise about the speed, i.e. we have no good knowledge of the speed. This then means we can't say how long (time) the electron is there. Concluding: We could say that the electron was in the nucleus at the moment we measured its position, but we can't say anything more. Probably it just was there for some very short time, which we wouldn't consider an "electron in the nucleus". Am I dead wrong?

    @poolwin2001: Remember, [tex]\Delta v [/tex] is higher than c, not v. This result means you're measurement in speed is completely useless, because with an uncertainty higher than c it could be anything.
     
  21. Jul 26, 2005 #20

    Danger

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    In one way, you can consider that there are electrons in nuclei. That's going by the concept of a neutron being a proton and an electron combined, which isn't quite right but can be inferred from beta decay.
     
  22. Jul 26, 2005 #21

    ZapperZ

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    I brought up the example of wave mechanics since that is what most people are familiar with. I can easily do this via matrix mechanics JUST to satisfy Heisenberg. But what have I changed? Did I changed the definition of the HUP and how it is derived?

    Note that the HUP is NOT part of the standard postulate of QM. The HUP simply did not appear out of thin air as the "starting point". This is what most people (not you) who have not had any formal intro to QM do not understand. The HUP is treated as IF it is a stand-alone principle that was never derived. This is as accurate as using the time-dilation effect as the starting point for Special Relativity.

    But that is my whole point! You cannot simply say "oh, the confinment is just too small that the momentum just "blows up". As astute student will ask "well, what about the nucleons? They are confined to the same space. Why aren't their momentum blowing up?" In fact, the quark confiment is even MORE stringent than that, and one could also ask why haven't the quarks (being point particles as much as the electron) blow out of the nucleus? It is a different momentum and a different potential. The spatial confinment alone isn't sufficient to consistently explain everything.

    There's nothing wrong with what Feynman said, but one has to put it within the context of what is being illustrated.

    Zz.
     
  23. Jul 26, 2005 #22

    ZapperZ

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    I'm not sure what is there to correct since I find nothing wrong with that. Even neglecting any adjustments in the binding potential for nucleons, what you showed is perfectly valid.

    Zz.
     
  24. Jul 26, 2005 #23
    Well, if my explaination is not enough as Zapperz stated , I think this would help:

    This is the direct answer to your question(TheSpeed=DUCK!):

    "
    First of all you can neglect gravity in your question. As an exercise you might try computing the electrostatic attraction between an electron and a proton and compare it with the gravitational attraction. You'll see that gravity is many millions of times weaker.

    Still, why doesn't the electron end up in the nucleus with the proton? Well, first think about the solar system. Why doesn't the earth end up in the sun? The answer is angular momentum conservation. The earth has some large amount of angular momentum because we have velocity perpendicular to the line from the sun to us. Since angular momentum is conserved we stay in a stable orbit.

    Now, what about the atom? Early models of the atom treated the atom as a solar system and used the idea of angular momentum conservation to explain its stability. Then it was realized that if the electron is moving in a circle then it must be accelerating (even though the magnitude of its velocity may be constant, the fact that its velocity changes direction means it's accelerating). But all accelerated charges radiate energy. As it loses energy it loses angular momentum -- so it should spiral into the nucleus. The fact that there are any atoms at all was a great mystery at the turn of the last century -- it was one of the great problems that led to the development of quantum mechanics.

    In quantum mechanics angular momentum is not a continuous variable but it is quantized: it comes in integer multiples of a fundamental unit given by Planck's constant. Now if you're familiar with chemistry then you know about s-orbitals, p-orbitals, and so on. These are quantum-mechanical states of an orbiting electron, each with a different integer value of angular momentum. The 's' is for zero angular momentum, 'p' is for one unit and so on. Now if you have any angular momentum then you're safe because your wavefunction does not overlap the nucleus very much. That means it's pretty unlikely you'll ever find yourself in the nucleus to encounter a positively charged proton. The 's'-orbital states, however, actually do spend time in the nucleus! Why don't they annihilate with the protons?

    The answer is...they do! But very, very rarely. The process by which a proton absorbs an electron and becomes a neutron and a neutrino is known as 'inverse beta decay' and it does happen in some atoms occasionally. Fortunately, the force that governs this process is the weak force -- which got its name by being very, very weak. That means that despite the fact that some 's'-orbital electrons occasionally end up in the nucleus they rarely get absorbed by protons. Thus most atoms are stable and chemistry (and life) is possible.

    "



    Source: http://www.physlink.com
     
  25. Jul 26, 2005 #24

    OlderDan

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    The only issue I have is with the notion that the HUP is a "consequence" of something else. Whether the postulates of QM are stated in a wave or matrix formulation does not matter. The postulates themselves express a view that the universe behaves a certain way, or at least that it can only be observed in certain states. These postulates reflect an inherent uncertainty in the outcome of an observation. While it may be true that one needs to use a formalism that has proven effective to quantify the degree of indeterminism, it does not speak to the fundamental reason why a particle's postion/momentum or energy/time must have a degree of uncertainty.

    When I refer to the HUP I am not just talking about a mathematical equation one uses to calculate the limits of precision to which a particle's parameters can be known. I have no problem with the idea that the equation is derived any more than I have a problem with the value of c needing to be measured or derived from other measured quantities. To me that is a very different issue from whether uncertainty is a fundamental property of matter and energy that leads to the quantization of measured parameters, or vice-versa. I don't see the absence of an explicit statement of uncertainy among the postulates as proof that uncertainty is not a fundamental property of the universe on an equal level with the constancy of light speed to all inertial observers. It is in that sense that I question the idea that "uncertainty" is a consequence of something more fundamental, and hence not a principle in its own right.
     
  26. Jul 26, 2005 #25

    ZapperZ

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    Er.. back up a bit. Now it is my turn to say that no one is saying such a thing. As much as time dilation CANNOT be avoided in SR, the same thing can be said about the HUP. In fact, within my explanation of the HUP both in another parallel thread currently ongoing in PF AND in my journal entry, I tried to make sure to emphasize that it is a INHERENT property of QM observables and NOT simply and trivially a DETECTION accuracy!

    Maybe people, when confronted with the HUP, would produce an example along the line that says "if you want to measure the position of an electron, you have to use photons with shorter wavelength, but this means the photons will have higher energy, and because of that, the act of measurement will cause the electron to get deflected severely and thus, we lose info about its momentum". THIS is what a lot of people use to justify the HUP. This is false! It REDUCES the HUP to simply out technological shortcoming of measurement and NOT something inherent. This is NOT what I am saying at all!

    Again, the single slit diffraction experiment is the clearest example of the HUP at work at the macroscopic level. It is the most direct illustration of how fundamental and inherent a property it is. However, it isn't the starting point for the formulation of QM the same way time dilation isn't the starting point of SR. They are inherent, yes, but they do not appear out of nowhere within the formulation. Saying this does not delegate them to second class citizens.

    Zz.
     
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