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Why is a hydrogen atom lighter than a electron and a proton

  1. Jul 20, 2012 #1
    What exactly is it that makes the energy/mass of a hydrogen atom be lower than that of the electron and proton separately?
    I am aware that this process is what causes stars to emit light, during nuclear fusion deuterium has a smaller mass than a proton and a neutron so its extra mass/energy is emitted as light.
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  3. Jul 20, 2012 #2


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    The binding energy of the electron in hydrogen is 13.6 eV. By Einsteins E=mc^2 this corresponds to a tiny mass difference.
  4. Jul 20, 2012 #3
    So some energy is taken from the electron and used as binding energy?
  5. Jul 20, 2012 #4


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    No, that's not it.

    When you combine an electron and a proton to form a hydrogen atom, the reaction gives off energy. At least part of that energy comes from the electrostatic attraction between the two component pieces.

    Energy is conserved.

    That means that once this extra energy has radiated away (as heat, photons or whatever), the resulting hydrogen atom will have less total energy than the electron and the proton from which it was assembled.

    By E=mc^2, this lost energy manifests as lost mass. The composite has less mass than the sum of the parts from which it was assembled.

    The term "binding energy" refers to how much energy is released when a bond is formed or, equivalently, how much energy would need to be injected to break a bond. If were able to measure carefully enough you would find that binding energy is always accompanied by a "mass defect".
  6. Jul 20, 2012 #5


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    No, the energy is taken from the electric field surrounding both the electron and the proton.
    The electromagnetic field is smaller in the atom than for the isolated electron and proton.
  7. Jul 20, 2012 #6
    thank you both :).
  8. Jul 21, 2012 #7


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    And that "binding energy" is due to electric fields, in the case of an atom, as stated already. Inside a nucleus there are other forces, so the binding energy is due to them also.
  9. Jul 21, 2012 #8
    So gluons, W and Z particles are also the cause?
  10. Oct 30, 2012 #9
    The hydrogen atom is NOT LIGTER.

    Starting with an electron and proton at near infinity, the coulomb potential force causes the electron to accelerate (gain energy) toward the proton and vis-versa and the electron/proton system gains 27.2 eV (e^2/Bohr_R). Only half that energy 13.6 eV, is emitted by the hydrogen stom. So the hydrogen atom is heavier by 13.6 eV. Remember any energy in an object, even heat energy makes the object heavier.

    Unfortunately the measured hydrogen-1 mass (that I have seen) is not accurate enough by several orders of magnitude to measure this difference in mass.
  11. Oct 30, 2012 #10

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    Of course it is. I have to add energy to separate the electron from the proton.
  12. Oct 30, 2012 #11


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    Then why do I not see hydrogen atoms spontaneously emitting a 13.6 eV photon as they decay into an unbound proton and electron?
  13. Oct 30, 2012 #12


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    The rest mass of the proton and electron compared to the rest mass of the hydrogen atom is what we mean by mass here. In your example you could have the extra energy left over as kinetic energy, but when we slow it down and measure it, it's mass is indeed less.
  14. Nov 4, 2012 #13
    Do the calculation to move an electron from the Bohr radius to infinity, i.e e^2/bohr_R = 27.2

    It takes 27.2 eV to move an electron from the Bohr radius to infinity !!!

    The photon energy you are adding is only 13.6 eV. Where do you think the other 13.6 eV comes from?
    Last edited: Nov 4, 2012
  15. Nov 4, 2012 #14
    The initial center of mass is not changed by the in-fall of the electron and proton as both accelerate toward each other. As the center of mass does not change, the hydrogen atom itself has no velocity nor kinetic energy.

    Thus all of the extra 13.6 eV is internal to the hydrogen atom, i.e. 13.6 eV heavier
  16. Nov 4, 2012 #15


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    The electron bound in a hydrogen atom already has 13.6 eV of kinetic energy. So you only need to add 13.6 eV to remove the electron.
  17. Nov 4, 2012 #16
    Exactly, what I have been saying.

    Just as nuclear kinetic energy makes the nucleus heavier than the sum of the proton and neutron masses, likewise the bound electron kinetic energy makes the hydrogen atom heavier than the mass of the isolated electron and proton.
  18. Nov 4, 2012 #17


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    Now you're forgetting about the hydrogen atom's -27.2 eV of potential energy. Add that to the 13.6 eV of KE, you get a total bound energy of -13.6 eV. So the hydrogen atom has lower energy than and is lighter than the isolated electron and proton by 13.6eV/c2
  19. Nov 5, 2012 #18


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    No, it is the other way round. Helium-4 is lighter than 2 protons plus 2 neutrons, for example.

    Proton mass: 1.007 276 u
    Neutron mass: 1.008 665 u
    Helium-4 mass: 4.002 603 u
  20. Nov 5, 2012 #19
    My apologies about nuclear mass, which is not a negative coulomb attraction binding process (which happens to add more energy than it emits) and is a true energy emission and removal binding process which does make the nucleus lighter than its constituents.
  21. Nov 5, 2012 #20
    My apologies on nuclear binding energy. Unlike the negative coulomb "binding" situation of the electron and proton of the hydrogen atom, in which the attractive forces that bring the electron and proton together and adds more energy than it emits, the nuclear process of bringing both protons and neutrons together adds no energy and thus the energy loss on nuclear binding of protons and neutrons does reduce mass.
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