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E=mc^2 question

  1. Nov 21, 2012 #1
    1. Energy is proportional to mass.
    2. Mass (of nucleus) is proportional to volume.
    3. Volume can be determined from cross-sectional area.

    If this is the case, then is E=mc^2 equivalent to kE=(pi)r^2 where r is the radius of the nucleus and k is some constant?
  2. jcsd
  3. Nov 21, 2012 #2


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    Is number 2 even correct? If I add one neutron to hydrogen to make deuterium, is the nuclear now bigger in volume?
  4. Nov 21, 2012 #3


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  5. Nov 21, 2012 #4
    Thanks, that helps.
  6. Nov 21, 2012 #5


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    Even if (2) were true (and DaleSpam has pointed out it isn't), you would expect an r3 term, not an r2 term. (Volume of a sphere isn't proportional to area).
  7. Nov 24, 2012 #6
    2. Mass = Volume x Density

    What's the idea to measure volume of as a cross section anyway?
    Volume of n-sphere can be easily calculated without any cross sectional area using formulas.
    Cross section of 4D objects is 3D object.

    I have no idea how to calculate mass-radius relationship for nucleus, it's difficult because it's a compound, but for example mass of electron = coupling * Planck's mass * Planck's length / classical electron radius
  8. Nov 24, 2012 #7


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    I think Andy Lee meant the two-dimensional cross-section which can be observed in particle physics - this can be used to estimate the volume of the nucleus.
  9. Nov 26, 2012 #8
    If 2. were correct I dont think atomic bombs would exist (at least not in the way they do in this universe!) since the energy as I understand it comes from the difference in mass of the nucleus and the constituents of the nucleus, so if they were proportional there wouldn't be any release of excess energy.
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