1
$\begingroup$

I'm curious approximately how much energy would be stored in the repulsion (both classical electrostatic, and any Pauli-type quantum effects) between the electrons if the "space" between the electrons and nuclei were shrunk down like this. How would it compare to, e.g., an atomic bomb being detonated, or the kinetic energy of the Earth orbiting the Sun?

This is essentially a Fermi problem likely suitable for an astrophysics course that includes white dwarf formation. The details of the "golf ball" and "grain of sand" are probably not critical, but if specifics are desired: A standard golf ball has a mass of 46 g, a diameter of 43 mm, and is mostly made of hydrocarbon polymers; a grain at the boundary between ISO 14688 medium and coarse sand has a diameter of 0.63 mm.

Improve this question
$\endgroup$
3
  • 8
    $\begingroup$ You would get the same energy that you used to shrink it $\endgroup$
    – vengaq
    Commented Oct 23, 2022 at 20:23
  • 1
    $\begingroup$ @vengaq: That's on the one hand trivially true--on the other hand it isn't. In other words, if it went precisely back to being the same golf ball then that would be true. On the other hand, compressing it that much would quite clearly break all chemical bonds, and presumably upon re-expanding, the nuclei and electrons would more likely settle into a state lower in energy (possibly something like a bunch of methane molecules). But in any case, that doesn't answer the question of how much potential energy the compressed cloud of nuclei and electrons has. $\endgroup$
    – biohacker
    Commented Oct 25, 2022 at 7:21
  • $\begingroup$ @ biohacker It seems to me that the only way to provide more "details or clarity" is to at least partially include the answer in your question. But if you knew enough to do that, I assume you wouldn't have asked the question! I estimate your compressed ball would release about $\sim10^{11}\,\textrm{J}$, which is about 30 tonnes TNT equivalent. Check out Is a small fragment of a white dwarf stable? and the associated neutron star question, and if you can't figure out the calculation you could try one last time to get this question reopened. $\endgroup$
    – David Bailey
    Commented Oct 26, 2022 at 3:03

0

Reset to default