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Can electron revolving around atom become source of gravity.?

  1. Jun 3, 2012 #1
    we know electron revolves around nucleus at nearly (1/100)th of light speed..does this mean electron as very high relativistic mass such that It can become local source of gravity..but this is not the case..why is this so.?
     
  2. jcsd
  3. Jun 4, 2012 #2

    Ger

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    Because it is not 'revolving' around the nucleus, like moon is around earth. Around the nucleus there is a charge distribution of excatly the same number of electric charges as in the nucleus, but of opposed charge. The racing around a nucleus would give rise to "Bremsestrahlung", the electron losing energy (by emiting photons) and drop into the kernel. Think electron (charge distribution) as a standing wave around a nucleus. Perfectly at rest. The mass of the electron allows for only a number of 'fitting' standing waves.
     
  4. Jun 26, 2012 #3
    The instruments at present can't measure the gravity caused by one electron. The increase in gravitational mass due to the change in velocity would be even harder to measure. As we shall see, the change in mass of an electron in an atom due to high velocity are very small compared to the rest mass of the electron. However, instruments for measuring emission spectra are much more sensitive than instruments for measuring gravity.
    Therefore, an equally interesting question is what would be the effect of the high velocity of the electron on the emission spectrum of the atom. So this post will address the effects of relativistic mass on the spectrum of electromagnetic radiation emitted from atoms.
    As another poster pointed out, stating that the electron "moves" is not precisely true. You are using a semiclassical approximation of quantum mechanics. However, the semiclassical approximation is accurate under certain conditions. Special relativity is completely consistent with quantum mechanics, both with quantum electrodynamics and in the semiclassical approximation. This post discusses the emission spectrum of atoms in terms of the semiclassical approximation of quantum mechanics, not in terms of QED.
    The velocity of the electron in a hydrogen atom, (1/100)th of light speed, is not close to the speed of light. The effect of speeds that are small compared to the speed of light is approximately half the square of the ratio between that speed and the speed of light. So if that ratio is much less than one, the effect of that speed on mass is much much less than one.
    If you substitute the velocity of the electron into the formula for relativistic mass, you will find that the difference between an electron moving at (1/100)th of light speed and an electron at rest is only (1/20000)th the mass of the electron at rest. This is a small amount and is very difficult to measure. The changes in the spectroscopy of the hydrogen
    A related question is: Does special relativity ever cause the spectrum of an atom to change from the hypothetical "nonrelativistic atom?"
    The answer is yes, but the difference is small. There is something called the Lamb shift, which is a very small splitting seen in the spectrum of a hydrogen atom. The Lamb shift is usually analyzed using QED. However, there may be a semiclassical analysis of the Lamb shift somewhere. The Lamb shift is basically caused by the small change in mass caused by special relativity. The Lamb shift has been measured, but it is tiny.
    Atoms of large atomic number sometimes show a larger shift in their spectrum for electrons that jump to an inner shell of the atom. This is because the electrons in the inner shell are moving closer to the speed of light. Instead of (1/100)th of light speed, the inner shell electron may be moving at (1/10)th of light speed. Again, the percentage change in frequency is small. The change in mass of an electron moving at (1/10)th of light speed would only be (1/200)th the rest mass of the electron. This is not a "high relativistic mass". However, one could consider it a "low relativistic mass".
    So the answer is that special relativity does effect the emission spectra of atoms, but very slightly. The spectra of atoms has been measured with great precision under highly controlled conditions. The experimental spectra do agree more with the spectra as predicted with Lorentzian invariance (i.e., relativistic) than with Galilean invariance (i.e., nonrelativistic).
     
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