Simplistically speaking, the electrons whirl around the nucleus very rapidly in all directions and by that motion create an outer shell to the atom. Compared to the size of the whole atom, the nucleus is tiny. The largest nuclei have a diameter of considerably less than one ten thousandth the diameter of the whole atom. In the case of hydrogen, which has the smallest nucleus, its diameter is closer to one hundred thousandth the size of the atom.
This may not sound like much. But consider the following facts. If the sun were the nucleus of a larger atom, its electron(s) in the outer shell would be considerably more than 10 billion miles out in space, well over three times the distance that the planet Pluto is actually away from the sun. By this standard, the earth is extremely close to the sun. It is only 107 times the sun's diameter away from it.
Looking at it somewhat differently, there is enough space within the atom to place between one trillion and one quadrillion nuclei in it. In other words, an atom is hardly a solid object. It contains very little stuff that we can call matter. Most of it is empty space.
How real is matter?
This has tremendous implications for an understanding of the world we live in. The impression we receive from our sensory contact with the world is that the world around us has substance. Things are solid. They are massive. They are real. The reality however is quite different. Everything is really massive emptiness.
Calculations made elsewhere show that the universe as a whole is mainly empty space with only small pockets of matter, galaxies of stars, spread out thinly within it. The galaxies too consist mainly of empty space. The stars within them are relatively few in number and small compared to the vastness of the empty zones between them. Now we see that even what seems to us to be really solid is ephemeral, a mirage, not at all what it appears to be. Not only is there space between the atoms and the molecules, that make up solid matter, but the atom itself can hardly be considered truly substantive. It too is comprised almost exclusively of emptiness, of void. The portion within it that constitutes real matter occupies only a minute fraction of the total space it fills.
Compressing atoms together
A simple calculation will drive this point home with incredible force. Let us imagine that we could strip all atoms of their electrons. In fact this sort of thing happens under intense conditions found in some stars. Let us also suppose that we could now tightly pack together all these stripped atoms, which would now consist only of the nuclei of these atoms. We would place all nuclei right next to each other. This too actually occurs under certain conditions. How much space would all the atoms of the earth occupy? Of a star? Of a galaxy? Of the universe? The calculations are not difficult to make.
Consider first that 90% of all atoms in a typical star and also in the universe as a whole are hydrogen atoms. An atom of hydrogen generally contains only one proton in its nucleus and has only one electron orbiting around this nucleus. A proton is roughly one hundred thousandth the size of the hydrogen atom.
That means that we could tightly pack about one quadrillion (1015) protons into the space occupied by a single hydrogen atom.
We also know that atoms are extremely small objects. There is enough space in one cubic inch to hold about 1.56 x 1025 hydrogen atoms. In sum this means that one cubic inch of space can conceivably hold on the order of 1040 protons or nuclei of hydrogen.
Compressing the sun
In all, the sun contains about 1057 atoms, most of which are hydrogen. So all we need is about 1017 cubic inches to pack all its nuclei together. This works out to be a cube of about 7.3 miles in all directions.
Compressing the Earth
The earth is considerably smaller than the sun. Although it has much heavier atoms, its total mass is still only about one three hundred and thirty thousandth the mass of the sun. Since protons and neutrons contribute almost all the mass of an atom and since protons and neutrons have about equal mass, this means that the total number of protons and neutrons in the sun are 330,000 as plentiful as all the protons and neutrons in the earth. Thus, all the nuclei in the earth's atoms could fit into a space that is about one third of a million the size just calculated. This works out to be a cube less than 560 feet in all directions.
Compressing the galaxy
The total mass of our galaxy, which is thought to be one of the larger ones, is anywhere from 100 billion to 2 trillion times the mass of our sun. If we use the upper number, 2 trillion, for our calculation, the total space occupied by all the protons and neutrons of the our entire galaxy would be 2 trillion times the cube of 7.3 miles that the sun's nuclei would occupy. This sounds extremely large. But remember how small things multiplied sometimes gives very big numbers.
The opposite is true for division. Two trillion cubes each 7.3 miles long, wide and deep can be fit into a larger cube that is less than 100,000 miles in all directions. In actuality the sun occupies vastly more space. Its diameter is 864,000 miles. We could fit all the atoms in about 3500 galaxies the size of ours into the space the sun alone occupies.
Compressing the universe
How about the universe? The calculation is trivial. Roughly estimated, the total amount of mass in the universe is about 100 billion times the mass of our galaxy. So we would need that many cubes each 100 thousand miles in all directions. A very large cube about 450 million miles in all directions would be large enough for this task. Four hundred and fifty million miles is somewhat less than the distance from the sun to the planet Jupiter. Put somewhat differently. If instead of making our container cubical, we would make it cylindrical placing its center where our sun is and its extremities in the zone where the planet Pluto orbits, all the nuclei of the universe would fit into this box if it were a little more than 2 million miles deep. In other words, by giving it just a bit of three dimensionality our solar system becomes more than large enough to accommodate all the stuff of the universe.
Compressing ourselves
It is not very pleasant to consider how small we would become if we were reduced the same way. So I will not do the calculation.
Hint for all the masochists out there: Find out how many cells there are in a person and determine the size of a cell. Figures for both these are given elsewhere.