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Dr. Christopher S. Baird

Do atoms ever actually touch each other?

Category: Physics      Published: April 16, 2013

two hydrogen atoms
Artistic rendering of two hydrogen atoms moving close to each other. At what point do they "touch"? It depends on what you mean by touch. Public Domain Image, source: Christopher S. Baird.

The answer depends on what you mean by "touch". There are three possible meanings of touch at the atomic level: 1) two objects influence each other, 2) two objects influence each other significantly, or 3) two objects reside in the exact same location. Note that the everday concept of touch (i.e the hard boundaries of two objects exist at the same location) makes no sense at the atomic level because atoms don't have hard boundaries. Atoms are not really solid spheres. They are fuzzy quantum probability clouds filled with electrons spread out into waving cloud-like shapes called "orbitals". Like a cloud in the sky, an atom can have a shape and a location without having a hard boundary. This is possible because the atom has regions of high density and regions of low density. When we say that an atom is sitting at point A, what we really mean is that the high-density portion of the atom's probability cloud is located at point A. If you put an electron in a box (as is done in quantum dot lasers), that electron is only mostly in the box. Part of the electron's wavefunction leaks through the walls of the box and out to infinity. This makes possible the effect of quantum tunneling, which is used in scanning tunneling microscopes. With the non-solid nature of atoms in mind, let us look at each of the possible meanings of touching.

1. If "touching" is taken to mean that two atoms influence each other, then atoms are always touching. Two atoms that are held a mile apart still have their wavefunctions overlapping. The amplitude of one atom's wavefunction at the point where it overlaps with the other atom's center will be ridiculously small if they are a mile apart, but it will not be zero. In principle, two atoms influence each other no matter where they are in the universe because they extend out in all directions. In practice, if two atoms are more than a few nanometers apart, their influence on each other typically becomes so small that it is overshadowed by the influence of closer atoms. Therefore, although two atoms a mile apart may technically be touching (if we define touching as the overlap of atomic wavefunctions), this touching is typically so insignificant that it can be ignored.

What is this "touching"? In the physical world, there are only four fundamental ways for objects to influence each other: through the electromagnetic force, through the strong nuclear force, through the weak nuclear force, and through the force of gravity. Neutrons and protons that make up the nucleus of an atom are bound to each other and undergo reactions via the two nuclear forces. The electrons that make up the rest of the atom are bound to the nucleus by the electromagnetic force. Atoms are bound into molecules, and molecules are bound into everyday objects by the electromagnetic force. Finally, planets (as well as other large astronomical objects) and macroscopic objects on the planet's surface are bound together by gravity. If two atoms are held a meter apart, they are touching each other through all four fundamental forces. However, for typical atoms, the electromagnetic force tends to dominate over the other forces. What does this touching lead to? If two atoms are too far apart, their interaction is too weak compared to other surrounding bodies to amount to anything. When the two atoms get close enough, this interaction can lead to many things. The entire field of chemistry can be summed up as the study of all the interesting things that happen when atoms get close enough to influence each other electromagnetically. If two atoms are non-reactive and don't form covalent, ionic, or hydrogen bonds, then their electromagnetic interaction typically takes the form of the Van der Walls force. In the Van der Walls effect, two atoms brought close to each other induce electric dipole moments in each other, and these dipoles then attract each other weakly through electrostatic attraction. While the statement that "all atoms on the planet are always touching all other atoms on the planet" is strictly true according to this definition of touching, it is not very helpful. Instead, we can arbitrarily define an effective perimeter that contains most of the atom, and then say that any part of the atom that takes extends beyond that perimeter is not worth noticing. This takes us to our next definition of touching.

2. If "touching" is taken to mean that two atoms influence each other significantly, then atoms do indeed touch, but only when they get close enough. The problem is that what constitutes "significant" is open to interpretation. For instance, we can define the outer perimeter of an atom as the mathematical surface that contains 95% of the atom's electron mass. As should be obvious at this point, a perimeter that contains 100% of the atom would be larger than the earth. With 95% of the atom's electron probability density contained in this mathematical surface, we could say that atoms do not touch until their 95% regions begin to overlap. Another way to assign an effective edge to an atom is to say it exists halfway between two atoms that are covalently bonded. For instance, two hydrogen atoms that are covalently bonded to each other to form an H2 molecule have their centers separated by 50 picometers. They can be thought of as "touching" at this separation. In this approach, atoms touch whenever they are close enough to potentially form a chemical bond.

3. If "touching" is taken to mean that two atoms reside in the exact same location, then two atoms never touch at room temperature because of the Pauli exclusion principle. The Pauli exclusion principle is what keeps all the atoms in our body from collapsing into one point. Interestingly, at very low temperatures, certain atoms can be coaxed into the exact same location. The result is known as a Bose-Einstein condensate.

Again, atoms never touch in the everyday sense of the word for the simple reason that they don't have hard boundaries. But in every other sense of the word "touch" that has meaning at the atomic level, atoms certainly touch.

Topics: Pauli exclusion principle, atom, atoms, do atoms touch, electromagnetism, electron, empty space, orbital, quantum, touch, wavefunction