Re: Space between the nucleus and electron in comparison to particle size?

Dear Ian,

At its present density, the nuclear matter that makes up the Universe
could definitely NOT fit into a cube with edge length 1 cm.  In fact,
such a cube could not even contain the nuclear matter in the Earth.

The protons and neutrons which comprise the nuclei of all atoms in the
Universe are tiny spheres of radius approximately 1 fermi = 1 femtometer
= 10^-15 meter (neglecting quantum mechanical fuzziness).  The masses
can be measured much more precisely:
   proton mass = 1.67262158 x 10^-27 kg
   neutron mass = 1.6749286 x 10^-27 kg
The density of nuclear matter is roughly 4 x 10^17 kg/m^3.  For
comparison, the density of water in these same units is 1000 kg/m^3.

To calculate the edge length L in meters of a cube containing only the
nuclear matter of any object of mass M in kilograms, use this formula:
        L = ( M / 4x10^17 )^1/3
Using the Earth with mass M = 5.974 x 10^24 kg, we get L = 246 meters.

It has been estimated that the Universe contains about 10^80 particles,
give or take a few orders of magnitude.  If all of this matter were
collected into a cube, then one side of this cube would measure about
4.5 x 10^11 meters.  Such a cube, centered on the Sun, would just fit
within the orbit of Mars.

The first words of my response were "At its present density", so now
let me explain the caveat.  During the massive explosion in which the
Universe was created, the Big Bang, the density of the Universe was
very much higher than current nuclear density.  A mere 10^-33 seconds
after its birth, the Universe would have been able to fit inside a cube
of edge length 1 cm.  In fact, before only 10^-35 seconds after its birth,
the entire Universe would have fit inside a present-day proton!
Reference http://casswww.ucsd.edu/public/tutorial/BB.html

--Randall J. Scalise    http://www.phys.psu.edu/~scalise/