Interest in physics

There was a bit of a weird call to the lab this morning. Someone was looking for my professor to ask him a couple questions he seemed curious about. I’ll have to paraphrase, but it went something like:

I’ve heard that the atom is something like 99% empty space, is that right? And also, would that be like our solar system, because I’ve heard it’s a lot of empty space too?

After I answered yes to these two questions (since I was a little taken aback by questions like this in the morning), he said thanks and hung up. My conclusion is he is just very interested in science, and I have to commend that.

But coming back to it, I want to go a little deeper into these questions.

First on the atom. We (generally) all know that atoms are small particles which make up all forms of matter. Atoms are made of electrons, neutrons and protons. The neutrons and protons form the nucleus, or core, of the atom, and the electrons orbit the core (kind of).

Let’s try to get a rough idea for the size of an atom. The volume is known, and is roughly around an Angstrom (or 1/10th of a nanometre depending on the atom). If we assume an atom like Helium, which has two protons, two neutrons, and two electrons, we can start getting some numbers.

The radius of a proton is roughly a femtometre (10^-15 m), and since the mass of a neutron is the same, it is also around a femtometre.

The electron is a bit trickier. Scientists originally guessed the radius of the electron by measuring its electrostatic force with other particles. Unfortunately, the electron is really small and very electrified. Therefore they were likely off, and many modern physicists consider the electron to be an infinitesimally small point particle (or as near as we can achieve). But to get a rough calculation of the “empty space” of an atom, let’s use the classical electron radius of 3 fm (notice that this is larger than the protons and neutrons, which are orders of magnitude heavier, a clue that the electron is likely smaller).

Now, the volume of a sphere is equal to 4/3 times pi times the radius cubed. However, we want the ratio of the stuff inside to the atom, so the 4/3 times pi cancels. Our result is then (for Helium):

(2*((1e15)³+(1e15)³+(3e15)³) )/(1e-10)= 0.0001=0.01%

This means that the helium atom is over (because I did some rounding up) 99.99% empty space!

To further blow your mind, remember that in solids (and especially in liquids and gases) atoms are not like plastic balls touching – they are in fact separated by some finite amount of space.

So when you look around, you’re seeing light (photons) interacting with less than 0.01% of what you see.

Now, how does this compare to the solar system?

First, I’m going to treat the solar system slightly differently. Because all of the planets fall along the same plane I’ll look first at the area of the plane that’s empty, and then at the entire “sphere” of the solar system.

I’m also going to ignore the asteroid belt. I had considered assuming it to be a solid belt, but considering the number of satellites that have passed through without harm, and the fact Ceres, the largest asteroid is under 1000 km in diameter, I feel justified in this. As well the moons of the various planets will be ignored, there are 166 observed, but I feel this will be justifiable by the size comparison. This calculation is meant to be fairly rough and to just give an estimate to the ratio.

I should also say that we do not really have an exact definition for the “radius” of the solar system. It’s speculated that the sun’s gravitational field is experienced 2 light years away in the nearby systems, but this distance would trump any calculations I attempt. I will use the heliopause as a rough outer shell, which is estimated to be 95 au’s away (an au is an astronomical unit, or the distance from the Earth to the sun, 150 million km).

So now we need the radii of the various planets and the sun (all rounded):

First thing we notice is that the sun is more than 99.99% (the ratio is about 1×10^-12) of the area of the stuff in “disk” of the solar system (my planar solar system), the numbers even larger for the “sphere”. So really, to get any idea of how much empty space there is, we could neglect everything except the sun and still have a pretty good estimate!

But to continue, the ratio of the “areas” of the sun to the entire solar system (since we can safely neglect everything else) is around 10^-9. And the ratios of the volumes is around 10^-13. These numbers are unfathomably small. If the solar system were a dartboard and you threw a dart at it, you would have a slightly better than 1 in a billion chance of hitting something.

So just try to keep in mind that almost everything in the entire universe, from the computer (or paper) you read this on to the farthest reaches of space is almost completely nothing.