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Thread: Atoms-Reason for the specific the 2,8,18… electron spread?

  1. #1 Atoms-Reason for the specific the 2,8,18… electron spread? 
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    Does QM have clarifications for the specific numerical electron spread over the shells ?

    Secondly , does QM provide clarification for the specific shape of the orbitals, being the probability etc of electrons existing there ?


    Thirdly, does the 'attraction' between the nucleus and the electrons follow Newton's law in any way?
    If so, is that only experimentally or empirically derived ?





    Or is al of this derived from experiment,observation, empirical, theoretical derivation ?


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  3. #2  
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    Quote Originally Posted by Noa Drake View Post
    Does QM have clarifications for the specific numerical electron spread over the shells ?

    Secondly , does QM provide clarification for the specific shape of the orbitals, being the probability etc of electrons existing there ?


    Thirdly, does the 'attraction' between the nucleus and the electrons follow Newton's law in any way?
    If so, is that only experimentally or empirically derived ?





    Or is al of this derived from experiment,observation, empirical, theoretical derivation ?
    Not sure what you are getting at in your first question - can you elaborate?

    Secondly, yes, QM certainly does provide the shape and density of electron probability distributions in each shell and subshell. That is exactly what the solutions to the time-independent Schroedinger equation for an atom do.

    Thirdly, yes, the potential well experienced by an electron due to the presence of an atomic nucleus, and the balance between kinetic and potential energy according to the electron's position within the potential well, is defined according to Newtonian mechanics. Where Newtonian mechanics ceases to apply is if any attempt is made to measure the position and momentum of the electron at any specific time. The wave-particle duality that underpins QM prevents knowledge of this.

    But you mention empirical derivation. Perhaps the most important respect in which empirically it was found that classical theory had to be abandoned, is that the classical predictions of Maxwell regarding radiation of energy by a moving charge are not obeyed. If electrons were point charges in classical orbit around the nucleus, they should continuously radiate energy and spiral into the nucleus. Obviously they don't: instead they either just stay at the same energy level, or clunk suddenly from one state to another, emitting or absorbing quanta of radiation when they do so. The fact the the energy emission or absorption occurs in this discontinuous manner was one of the spurs to the development of QM. (Others came from things such as the photo-electric effect and problems with the classical theory of black body radiation.)


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  4. #3  
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    Quote Originally Posted by exchemist View Post
    If electrons were point charges in classical orbit around the nucleus, they should continuously radiate energy and spiral into the nucleus.
    I've heard this many times but I never figured out the principle behind it.. could you please explain it to me, or just point me to some reading about this manner? Thanks very much.
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    Quote Originally Posted by Noa Drake View Post
    Does QM have clarifications for the specific numerical electron spread over the shells ?
    I assume this is a reference to the thread title. This is basically down the Pauli exclusion principle: no two electrons can have the same quantum state. The first shell has only one state so you can have one spin-up and one spin-down electron. The later shells have more degrees of freedom, so you can have more pairs of electrons. (That is my rough understanding; embarrassingly, I never did really get to grips with this, even after several years of physical chemistry.)
    ei incumbit probatio qui dicit, non qui negat
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    Ok, so

    -I know what Schrodinger defined there (the basics of it that you take a sphere and then with 2 angles from the centre out, you can establish every point in the sphere volume, developed further into more complex shapes from there, visualising the probability distribution of where to find the electrons.), but were these shapes came from, that is the why, the origin, the coming into existence of the specific areas or trajectories taken by the electron, is not known ?

    -The Newtonian correlation was observed empyrically, but no fysical explanation behind it was established or derived ?
    That is the why or how of that specific 'attractive drop' from the center outward, given the specific build of the atom.

    -And as for the spread of the electrons over the shells, the Pauli exclusion principle is the basis of the explanation for this in QM ?
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    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by Noa Drake View Post
    but were these shapes came from, that is the why, the origin, the coming into existence of the specific areas or trajectories taken by the electron, is not known ?
    The shapes of the orbitals are predicted by quantum theory. It is impractical to solve the equations exactly for anything much more complex than a hydrogen atom so various approximations are used, such as Hartree-Fock or density functional theory, for computational chemistry.
    ei incumbit probatio qui dicit, non qui negat
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    Quote Originally Posted by rickettsie View Post
    Quote Originally Posted by exchemist View Post
    If electrons were point charges in classical orbit around the nucleus, they should continuously radiate energy and spiral into the nucleus.
    I've heard this many times but I never figured out the principle behind it.. could you please explain it to me, or just point me to some reading about this manner? Thanks very much.
    Try googling for "Larmor radiation formula" or "radiation from accelerated charges."

    Antennas radiate EM energy because charges in the antenna undergo acceleration. A classical point electron in orbit around a nucleus is constantly accelerating, and thus would also radiate EM energy and quickly spiral in. The observed longevity of atoms tells us that the classical picture is faulty.
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  9. #8  
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    Quote Originally Posted by Noa Drake View Post
    Ok, so

    -I know what Schrodinger defined there (the basics of it that you take a sphere and then with 2 angles from the centre out, you can establish every point in the sphere volume, developed further into more complex shapes from there, visualising the probability distribution of where to find the electrons.), but were these shapes came from, that is the why, the origin, the coming into existence of the specific areas or trajectories taken by the electron, is not known ?

    -The Newtonian correlation was observed empyrically, but no fysical explanation behind it was established or derived ?
    That is the why or how of that specific 'attractive drop' from the center outward, given the specific build of the atom.

    -And as for the spread of the electrons over the shells, the Pauli exclusion principle is the basis of the explanation for this in QM ?
    1. Yes the origin of the shapes is understood. These are the 3D standing wave patterns you get as solutions to Schroedinger's equation. This equation, in its time-independent form, is an equation for standing waves. It was findings such as this that led people to understand sub-atomic particles as behaving in part like waves rather than as classical point particles. These shapes are actually very like the patterns of the waves in the standing-wave, resonant vibrations of a rubber ball. So, if electron probability distributions are like waves - which was the key QM insight - this is what you expect.

    2. I don't understand your question. The way electrostatic attraction varies with distance is Coulomb's Law, nothing to do with Newton: Coulomb's law - Wikipedia, the free encyclopedia.

    3. The distribution of electrons among shells and sub-shells is governed by two principles, first that electrons will fill the lowest energy levels first and only fill higher ones when the lower ones are "full", and second, Pauli's Exclusion Principle which says no two electrons can occupy the same quantum state. Since the quantum state is specified by the combination of the subshell occupied plus the spin orientation, it means in effect that 2 electron can occupy each subshell, so long as they have opposite spin orientations.
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    Ok, thank you.

    On point 2 above, coulomb's law does bear a striking resemblence to Newton's law.They may not be exactly the same, but the parallel should ring a few bells, instead of concluding that they have nothing to do with eachother, no ?

    On point 1 above : Standing waves : so interference has been measured, and the noninterfering areas are the orbital shapes ?
    Last edited by Noa Drake; January 25th, 2014 at 01:11 PM.
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  11. #10  
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    Quote Originally Posted by Noa Drake View Post
    Ok, thank you.On point 2 above, coulomb's law does bear a striking resemblence to Newton's law.They may not be exactly the same, but the parallel should ring a few bells, instead of concluding that they have nothing to do with eachother, no ?
    They both have an inverse square rule because space is 3 dimensional. As you increase the distance, the field (charge or gravity) is spread over a larger spherical area. The area is proportional to distance squared.
    ei incumbit probatio qui dicit, non qui negat
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    About the specific so-called magic numbers, these are partly governed by quantum numbers that identify the individual orbitals. In solving the time-independent Schrodinger equation for the hydrogen atom, the solution has to obey boundary conditions, and this gives rise to quantisation of the energy and angular momentum of the orbitals. This quantisation leads to three quantum numbers associated with each orbital:

    The principle quantum number
    The azimuthal quantum number
    The magnetic quantum number

    For the hydrogen atom, the principle quantum number determines the energy of the orbital and different values of the other two quantum numbers have the same energy. But for heavier atoms, as the electrons fill the lowest energy orbitals, due to electron-electron repulsion, and the different amount of penetration by the different orbitals to the shielded nuclear charge, the different values of the azimuthal quantum number have different energies. This means that the different orbitals fill in a particular order as the number of electrons (and the atomic number) increases. The magic numbers correspond to the number of electrons that give rise to the most stable noble gas configurations.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    The orbitals are filled in the following order as the atomic number increases:

    1s (2 electrons)
    2s (2 electrons)
    2p (6 electrons - 2px, 2py, and 2pz, 2 electrons each)
    3s (2 electrons)
    3p (6 electrons)
    4s (2 electrons)
    3d (10 electrons)
    4p (6 electrons)
    5s (2 electrons)
    4d (10 electrons)
    5p (6 electrons)
    6s (2 electrons)
    4f (14 electrons)
    5d (10 electrons)
    6p (6 electrons)
    7s (2 electrons)
    5f (14 electrons)
    6d (10 electrons)
    7p (6 electrons)
    etc
    There are no paradoxes in relativity, just people's misunderstandings of it.
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  14. #13  
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    Quote Originally Posted by Noa Drake View Post
    Ok, thank you.

    On point 2 above, coulomb's law does bear a striking resemblence to Newton's law.They may not be exactly the same, but the parallel should ring a few bells, instead of concluding that they have nothing to do with eachother, no ?

    On point 1 above : Standing waves : so interference has been measured, and the noninterfering areas are the orbital shapes ?
    Strange has dealt with point 2. I will just add that the area of a sphere is 4 pi r^2. So if you have a given intensity of something emanating from a point, then it will have spread out, at any radius r, by an amount related to 1/r^2. This is true of the intensity of light from the sun, or gravity, or electrostatic force, or anything like that. As Strange says, it is a consequence of 3D geometry rather than anything else.

    Re point 1, KJW has addressed this. However again I will add something. The way the numbers work out is to do with the harmonics of resonance in 3D. In a 1D piano or violin string you have a fundamental with one wavelength the whole length of the string, with no intermediate nodes of zero displacement. Then you have a series of harmonics, with 2 wavelengths separated by one node (octave above fundamental), 3 wavelengths separated by 2 nodes (octave + fifth above fundamental) and so on. But in the 3D rubber ball, you get the same thing but it is more complicated, because the nodes can either be radial (one or more concentric spherical shells at which there is no displacement) or angular (planes of zero displacement intersecting the centre of the ball). Or a combination of the two.

    Take the n=3 shell of the hydrogen atom. You can have the 3s subshell, in which you have a spherical distribution of electron probability but with 2 concentric radial nodes, or you can have the 3p, which has one angular node (plane passing through the nucleus) plus 1 radial node, or you can have the 3d, with 2 mutually perpendicular nodal planes through the nucleus and no radial nodes. With the p, you have 3 choices for where the nodal plane is, mutually at right angles. With the d, you have five choices for how to arrange the pairs of planes.

    In all options you have 2 nodes, but their arrangement in space varies. These are the possible resonances of the 2nd harmonic (3 wavelengths, 2 nodes) of a 3D system.

    So the numbers of orbitals arise quite naturally from how a series of harmonics builds up in 3D, for a spherically symmetrical resonator. It's all just the music of the spheres, if you like.
    Strange and KJW like this.
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    Ok, thank you , a very clear explanation of the build-up.
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    Quote Originally Posted by ASG141 View Post
    strange, there is this girl i'm involved with, she claims to be american, but you're so much like her.
    ….claims…..

    Not much of an involvement, then. But I suppose it would be by correspondence if one is not, at large, as it were.
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    why you deleting my posts? i did not ask her to come over and get naked did i. trust the yankee.....
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    i'm screwing her mum now, if you wanna so much correspondence, i'm running through yankee women.....lmao
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  19. #18  
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    Quote Originally Posted by ASG141 View Post
    i'm screwing her mum now, if you wanna so much correspondence, i'm running through yankee women.....lmao
    MODERATOR ACTION : Enough of this nonsense - you have been warned ( and suspended ) before for trolling; the minute you come back you start again. Banned, this time permanently.
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  20. #19  
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    It really was only going to be a matter of time. I can't decide whether they seriously need help or they think they are funny (which may also imply they need help, as a bipolar friend of mine said "mental illness is like a really exclusive in-joke, if you're the only one laughing you need help...")
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