Many books say that the hydrogen atom is basically empty space, as the nucleus is 100,000 times as small as the atom. This statement shows a serious misunderstanding of quantum mechanics and the role of measurement in physics. High school students should be presented with 20th century ideas and to be encouraged to think.

 

The atom is not mostly empty! The hydrogen atom is not a miniature solar system, with the electron going in orbit around the proton, with mostly empty space around the proton. Instead, the atom is a tiny blob, whose size is determined by the Heisenberg uncertainty principle and the binding energy of the electrons to the nucleus. The size of the nucleus is far smaller than the atom because of the huge energy of the nucleus. We know this from the fact that nuclear bombs release far more energy than chemical bombs.

 

This mistake is so very prevalent that we must discuss it carefully. What is meant by the size of an atom? Recall that when we ask a question in science, we must discuss how we measure it. See the discussion about mass. Mass is defined by using a scale (or measuring force and acceleration). Size of a small object is defined as what we measure using a microscope.

 

If we use an X-ray microscope so powerful that it can see objects smaller than the size of the atom, the X-rays will ionize the atom, making it impossible to speak about the size of the atom. The most powerful microscope that we can use that will not ionize the atom permits a resolution only of about an angstrom, the actual size of the atom. Quantum mechanics tells us that there is no meaning to size smaller than this atomic size, as there is no meaning to something that one cannot measure.

 

When we study the nucleus, on the other hand, we use much more powerful microscopes, particle scattering. We can see the small nucleus, while, of course, the atom is ionized. The reason we can see a much smaller nucleus is because the nuclear force is much stronger than the electrical force.

 

The size of the atom is not the same as the size of the nucleus as we use different measuring tools.

 

There is another way to look at the situation. We know about the wave-particle duality. If objects (light, helium atoms, or whatever) go through a double slit and fall on a photographic film, we see diffraction lines, indicating that the objects behave like waves. On the other hand, we can perform particle scattering, which means collisions of the objects (atoms scattering off each other), and note that the objects behave like particles. Particle scattering is similar to billiard balls bouncing off each other. An object is either a wave or a particle, depending on the measurement performed. The size of an atom also depends upon the measurement performed.

 

In summary, we must not confuse talk about the size of an atom with the size of the nucleus. We must not be carried away with our imagination, picturing an atom as a cloud containing a tiny nucleus. We can picture in our minds an atom, or we can picture a nucleus.

 

To clarify this some more, consider liquid helium, which remains liquid down to absolute zero. It becomes a superfluid at 2.17 kelvins because of quantum mechanics. The uncertainty principle tells us that we cannot specify the location of a helium atom with greater accuracy than the container. This means we cannot even imagine that the atoms are little balls bouncing around.

 

Superfluid helium is the clearest example of quantum mechanics. Teachers should discuss superfluid helium in order to help clarify quantum mechanics.

 

We must not shy away from dealing with superfluid helium, this very challenging topic. This discussion will force students to think about the meaning of reality, especially how reality depends upon measurements.