# Reduce sizing of molecule - Oxygen

Can the size of molecule oxygen reduce smaller? If yes, how is that possible? Is it related to proton and electron surrounding the nucleus?

Surprisingly enough, the answer is yes, though it would be extremely difficult in practice to reduce the size of a molecule as large as $\ce{O_2}$ by the method I will describe here.

First, I must be clear that "shrinking" as seen in many science-fiction stories is completely impossible. Size is not some arbitrarily determined parameter which you can change with a ray gun!

Though the concept of size is a little fuzzy at atomic/subatomic scales, we know it is the valence electrons who are responsible for determining the distance scales in atoms and molecules (since they're the farthest from the nuclei). After solving the Schrödinger equation for a system, one finds that the electrons are concentrated in regions around the nuclei called orbitals. A meaningful definition of size for these orbitals implies that they are around 100 picometres or more across, conveniently described as twice the Bohr radius.

Usually, this would be the limit for any atom or molecule. However, nature has a rather curious quirk. We have discovered that all atoms in the Universe involved in chemistry are made of electrons, protons and neutrons (the latter two being themselves made of different combinations of up quarks and down quarks). However, there are more subatomic particles out there, and there is nothing to stop (exotic) atoms being made out of these other subatomic particles, as long as they are combined in the right way.

Physics doesn't yet understand why, but the fundamental subatomic particles in the Universe come in three generations. That is, there are groups of particles which behave exactly the same (have the same spin, electric charge, among other parameters), but differ only in their mass. In particular, electrons are just one type in a group of three types of particles called leptons. The other types are called muons and taus (or tauons). Again, all leptons share exactly the same properties, except for mass; the muon is approximately 200 times heavier than the electron, while the tau is around 3500 times heavier. We don't naturally see atoms containing these heavier cousins of the electron because they decay very quickly and are hence much rarer. Even though the muon is one of the most stable subatomic particles, its mean lifetime is a mere $2.2\ \mu s$, and the tau is much more unstable still. In the case of the muon, however, it is long-lived enough to produce it artificially and get some chemistry done.

If one were to mix muons with normal atomic nuclei in an appropriate chamber, then for a fleeting moment it would be possible to make atoms and molecules where all the electrons are replaced with muons. The resulting atoms/molecules would have muon orbitals instead of electron orbitals. By solving the Schrödinger equation for muons instead of electrons (changing $m_e$ for $m_{\mu}\approx200\ m_e$), the Bohr radius becomes around 200 times smaller and as a direct consequence the muon orbitals are smaller by approximately the same factor. Thus, an oxygen atom where all electrons have been replaced by muons will be about 1/200th the size, but will display almost exactly the same chemistry; two such exotic atoms would be expected to combine exactly as normal oxygen atoms do, creating an $\ce{O_2}$ molecule with sixteen muons instead of electrons, with an expected bond length of around $0.6\ pm$ instead of the usual $121\ pm$.

This may all seem theoretical, but muonic atoms have already been made in the laboratory before. Given the difficulties in producing and manipulating muons in their short lifespan, the only atoms produced as of yet seem to be muonic hydrogen (where the single electron is replaced by a muon) and quite recently muonic helium where only one of two electrons was replaced with a muon. In the latter case, the mix of electrons and muons makes the atom behave chemically quite differently from regular helium or doubly-muonic helium.

If you could eliminate the Pauli exclusion principle then the size of all atoms and molecules would collapse. Because electrons cannot have the same four quantum numbers in an atom, $n$, $l$, $m_l$, and $m_s$, the electrons in multi-electron atoms and molecules are forced to occupy the higher energy and larger radius orbitals. More electrons: bigger atom.

http://www.grandinetti.org/Teaching/Chem121/Lectures/QuantumNumbers