# What do moles and moles of various subatomic particles gathered together look like?

I wonder whether it is even possible to find the answer. If it is impossible to find out, why?

Do moles of neutrons basically look like a neutron star? If so, what does one look like?

How about moles and moles of protons and electrons gathered together? What would be their electromagnetic attraction? What would be some of their properties?

What would be the explosive repulsion if you gathered a mole of electrons or protons together in one spherical ball?

• The Pauli Exclusion Principle keeps stuff like this from presenting a universally threatening problem. Thankfully gravity doesn't listen to anyone but itself and makes neutron stars in spite of the principle. – Jim Jun 18 '15 at 15:29
• look at the definition of mole en.wikipedia.org/wiki/Mole_%28unit%29 . Your question is not well defined. – anna v Jun 18 '15 at 16:14
• one mole of something (e.g moles) is just a number. 1 mole of moles is 6.02e23 moles. question is how dense you pack them – Oct18 is day of silence on SE Jun 18 '15 at 16:51
• @aaaaaa I think it uses "moles and moles" meaning multiple moles. Not meaning a mole of moles. Similar to how "dozens and dozens" doesn't mean 144 – Jim Jun 18 '15 at 17:20

## 2 Answers

If you had a mole of electrons and a mole of protons and put them together, they would make hydrogen. The transition from ions to ground-state atoms would release 13.6 eV/atom or about 1300 kJ/mol.

This mole of hydrogen would have a mass of one gram. For comparison, combustion of 1 kg of gasoline releases about 44 MJ of heat; your completely-ionized hydrogen would win in a fight.

Hydrogen atoms and hydrogen molecules don't interact strongly with visible light, so your sample would be invisible.

If you had a mole of free charges (electrons or protons, but not both) you would have a lot more energy. How much is a famous problem in electrostatics: the self-energy of a uniformly-charged sphere. You find it by computing the energy needed to assemble each thin shell that makes up the sphere and integrating over the volume; the solution is that the energy of the shell is $$U = \frac35 \frac1{4\pi\epsilon_0} \frac{Q^2}{R} = \frac 35 \frac{\alpha\hbar c}{e^2} \frac{Q^2}{R}$$ for charge $Q$, sphere radius $R$, fine structure constant $\alpha$. A mole of electrons in a sphere with one meter radius would have energy \begin{align} U &= \frac 35 \frac{ \rm 200\,eV\,nm }{137} \frac{ (6\times20^{23})^2 }{ 10^9\rm\,nm} \left( {}\times \frac{ \rm1.6\times10^{-19}\,J }{\rm 1\,eV} \right) \\ &\approx 10^{19}\rm\,J \end{align} Don't stand too close.

I assume that what you're getting at is something like "what would it look like if we created something the size and mass of a basketball, made of only neutrons?" If this is what you're getting at, you should consider what is meant by what something "looks like". This generally means how does visible wavelength light interact with it? A regular basketball absorbs and emits visible light such that the net result is perceived as and orange-brown sphere.

If the ball were made of neutrons, there would be essentially no interaction with visible light, and so the ball would be invisible.

For protons and electrons gathered together, the appearance would depend on temperature. For example, at some temperature it would be hot enough to significantly populate excited states of the H_2 molecule and you'd see pink light.

• If it was a dense ball of protons surrounded by electrons, it would technically be an atom with the largest atomic number on record. It would probably decay faster than we could see anything. Violently so. I'd warrant that anyone close enough to see it would die – Jim Jun 18 '15 at 17:24
• What would be the power of an explosively repulsing ball of quadrillions of electrons? – HyperLuminal Jun 18 '15 at 17:39